id	sid	tid	token	lemma	pos
ejpam-3759	1	1	european	european	PROPN
ejpam-3759	1	2	journal	journal	PROPN
ejpam-3759	1	3	of	of	ADP
ejpam-3759	1	4	pure	pure	ADJ
ejpam-3759	1	5	and	and	CCONJ
ejpam-3759	1	6	applied	apply	VERB
ejpam-3759	1	7	mathematics	mathematic	NOUN
ejpam-3759	1	8	vol	vol	NOUN
ejpam-3759	1	9	.	.	PROPN
ejpam-3759	2	1	13	13	NUM
ejpam-3759	2	2	,	,	PUNCT
ejpam-3759	2	3	no	no	INTJ
ejpam-3759	2	4	.	.	NOUN
ejpam-3759	2	5	3	3	NUM
ejpam-3759	2	6	,	,	PUNCT
ejpam-3759	2	7	2020	2020	NUM
ejpam-3759	2	8	,	,	PUNCT
ejpam-3759	2	9	620	620	NUM
ejpam-3759	2	10	-	-	SYM
ejpam-3759	2	11	630	630	NUM
ejpam-3759	2	12	issn	issn	PROPN
ejpam-3759	2	13	1307	1307	NUM
ejpam-3759	2	14	-	-	SYM
ejpam-3759	2	15	5543	5543	NUM
ejpam-3759	2	16	–	–	PUNCT
ejpam-3759	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3759	2	18	published	publish	VERB
ejpam-3759	2	19	by	by	ADP
ejpam-3759	2	20	new	new	PROPN
ejpam-3759	2	21	york	york	PROPN
ejpam-3759	2	22	business	business	PROPN
ejpam-3759	2	23	global	global	PROPN
ejpam-3759	2	24	almost	almost	ADV
ejpam-3759	2	25	bi	bi	ADJ
ejpam-3759	2	26	-	-	ADJ
ejpam-3759	2	27	γ	γ	NOUN
ejpam-3759	2	28	-	-	PUNCT
ejpam-3759	2	29	ideals	ideal	NOUN
ejpam-3759	2	30	and	and	CCONJ
ejpam-3759	2	31	fuzzy	fuzzy	ADJ
ejpam-3759	2	32	almost	almost	ADV
ejpam-3759	2	33	bi	bi	ADJ
ejpam-3759	2	34	-	-	ADJ
ejpam-3759	2	35	γ	γ	NOUN
ejpam-3759	2	36	-	-	PUNCT
ejpam-3759	2	37	ideals	ideal	NOUN
ejpam-3759	2	38	of	of	ADP
ejpam-3759	2	39	γ	γ	NOUN
ejpam-3759	2	40	-	-	PUNCT
ejpam-3759	2	41	semigroups	semigroup	NOUN
ejpam-3759	2	42	anusorn	anusorn	ADJ
ejpam-3759	2	43	simuen1	simuen1	PROPN
ejpam-3759	2	44	,	,	PUNCT
ejpam-3759	2	45	saleem	saleem	PROPN
ejpam-3759	2	46	abdullah2	abdullah2	PROPN
ejpam-3759	2	47	,	,	PUNCT
ejpam-3759	2	48	winita	winita	PROPN
ejpam-3759	2	49	yonthanthum1	yonthanthum1	PROPN
ejpam-3759	2	50	,	,	PUNCT
ejpam-3759	2	51	ronnason	ronnason	NOUN
ejpam-3759	2	52	chinram	chinram	PROPN
ejpam-3759	2	53	1,3,∗	1,3,∗	NUM
ejpam-3759	2	54	1	1	NUM
ejpam-3759	2	55	algebra	algebra	NOUN
ejpam-3759	2	56	and	and	CCONJ
ejpam-3759	2	57	applications	application	NOUN
ejpam-3759	2	58	research	research	NOUN
ejpam-3759	2	59	unit	unit	NOUN
ejpam-3759	2	60	,	,	PUNCT
ejpam-3759	2	61	prince	prince	NOUN
ejpam-3759	2	62	of	of	ADP
ejpam-3759	2	63	songkla	songkla	PROPN
ejpam-3759	2	64	university	university	PROPN
ejpam-3759	2	65	,	,	PUNCT
ejpam-3759	2	66	hat	hat	PROPN
ejpam-3759	2	67	yai	yai	PROPN
ejpam-3759	2	68	,	,	PUNCT
ejpam-3759	2	69	songkhla	songkhla	VERB
ejpam-3759	2	70	90110	90110	NUM
ejpam-3759	2	71	,	,	PUNCT
ejpam-3759	2	72	thailand	thailand	PROPN
ejpam-3759	2	73	2	2	NUM
ejpam-3759	2	74	department	department	NOUN
ejpam-3759	2	75	of	of	ADP
ejpam-3759	2	76	mathematics	mathematic	NOUN
ejpam-3759	2	77	,	,	PUNCT
ejpam-3759	2	78	abdul	abdul	PROPN
ejpam-3759	2	79	wali	wali	PROPN
ejpam-3759	2	80	khan	khan	PROPN
ejpam-3759	2	81	university	university	PROPN
ejpam-3759	2	82	,	,	PUNCT
ejpam-3759	2	83	mardan	mardan	NOUN
ejpam-3759	2	84	23200	23200	NUM
ejpam-3759	2	85	,	,	PUNCT
ejpam-3759	2	86	pakistan	pakistan	PROPN
ejpam-3759	2	87	3	3	NUM
ejpam-3759	2	88	centre	centre	NOUN
ejpam-3759	2	89	of	of	ADP
ejpam-3759	2	90	excellence	excellence	NOUN
ejpam-3759	2	91	in	in	ADP
ejpam-3759	2	92	mathematics	mathematic	NOUN
ejpam-3759	2	93	,	,	PUNCT
ejpam-3759	2	94	si	si	PROPN
ejpam-3759	2	95	ayuthaya	ayuthaya	PROPN
ejpam-3759	2	96	road	road	PROPN
ejpam-3759	2	97	,	,	PUNCT
ejpam-3759	2	98	bangkok	bangkok	PROPN
ejpam-3759	2	99	10400	10400	NUM
ejpam-3759	2	100	,	,	PUNCT
ejpam-3759	2	101	thailand	thailand	PROPN
ejpam-3759	2	102	abstract	abstract	NOUN
ejpam-3759	2	103	.	.	PUNCT
ejpam-3759	3	1	in	in	ADP
ejpam-3759	3	2	this	this	DET
ejpam-3759	3	3	paper	paper	NOUN
ejpam-3759	3	4	,	,	PUNCT
ejpam-3759	3	5	we	we	PRON
ejpam-3759	3	6	introduce	introduce	VERB
ejpam-3759	3	7	the	the	DET
ejpam-3759	3	8	notions	notion	NOUN
ejpam-3759	3	9	of	of	ADP
ejpam-3759	3	10	almost	almost	ADV
ejpam-3759	3	11	bi	bi	ADJ
ejpam-3759	3	12	-	-	ADJ
ejpam-3759	3	13	γ	γ	NOUN
ejpam-3759	3	14	-	-	PUNCT
ejpam-3759	3	15	ideals	ideal	NOUN
ejpam-3759	3	16	and	and	CCONJ
ejpam-3759	3	17	fuzzy	fuzzy	ADJ
ejpam-3759	3	18	almost	almost	ADV
ejpam-3759	3	19	bi	bi	NOUN
ejpam-3759	3	20	-	-	NOUN
ejpam-3759	3	21	γideals	γideal	NOUN
ejpam-3759	3	22	of	of	ADP
ejpam-3759	3	23	γ	γ	NOUN
ejpam-3759	3	24	-	-	PUNCT
ejpam-3759	3	25	semigroups	semigroup	NOUN
ejpam-3759	3	26	and	and	CCONJ
ejpam-3759	3	27	give	give	VERB
ejpam-3759	3	28	properties	property	NOUN
ejpam-3759	3	29	of	of	ADP
ejpam-3759	3	30	them	they	PRON
ejpam-3759	3	31	.	.	PUNCT
ejpam-3759	4	1	moreover	moreover	ADV
ejpam-3759	4	2	,	,	PUNCT
ejpam-3759	4	3	we	we	PRON
ejpam-3759	4	4	investigate	investigate	VERB
ejpam-3759	4	5	relationships	relationship	NOUN
ejpam-3759	4	6	between	between	ADP
ejpam-3759	4	7	almost	almost	ADV
ejpam-3759	4	8	bi	bi	NOUN
ejpam-3759	4	9	-	-	ADJ
ejpam-3759	4	10	γ	γ	NOUN
ejpam-3759	4	11	-	-	PUNCT
ejpam-3759	4	12	ideals	ideal	NOUN
ejpam-3759	4	13	and	and	CCONJ
ejpam-3759	4	14	fuzzy	fuzzy	ADJ
ejpam-3759	4	15	almost	almost	ADV
ejpam-3759	4	16	bi	bi	ADJ
ejpam-3759	4	17	-	-	ADJ
ejpam-3759	4	18	γ	γ	NOUN
ejpam-3759	4	19	-	-	PUNCT
ejpam-3759	4	20	ideals	ideal	NOUN
ejpam-3759	4	21	.	.	PUNCT
ejpam-3759	5	1	2020	2020	NUM
ejpam-3759	5	2	mathematics	mathematic	NOUN
ejpam-3759	5	3	subject	subject	NOUN
ejpam-3759	5	4	classifications	classification	NOUN
ejpam-3759	5	5	:	:	PUNCT
ejpam-3759	5	6	20m99	20m99	NUM
ejpam-3759	5	7	key	key	ADJ
ejpam-3759	5	8	words	word	NOUN
ejpam-3759	5	9	and	and	CCONJ
ejpam-3759	5	10	phrases	phrase	NOUN
ejpam-3759	5	11	:	:	PUNCT
ejpam-3759	5	12	bi	bi	ADJ
ejpam-3759	5	13	-	-	ADJ
ejpam-3759	5	14	γ	γ	NOUN
ejpam-3759	5	15	-	-	PUNCT
ejpam-3759	5	16	ideals	ideal	NOUN
ejpam-3759	5	17	,	,	PUNCT
ejpam-3759	5	18	almost	almost	ADV
ejpam-3759	5	19	bi	bi	ADJ
ejpam-3759	5	20	-	-	ADJ
ejpam-3759	5	21	γ	γ	NOUN
ejpam-3759	5	22	-	-	PUNCT
ejpam-3759	5	23	ideals	ideal	NOUN
ejpam-3759	5	24	,	,	PUNCT
ejpam-3759	5	25	fuzzy	fuzzy	ADJ
ejpam-3759	5	26	almost	almost	ADV
ejpam-3759	5	27	bi	bi	ADJ
ejpam-3759	5	28	-	-	ADJ
ejpam-3759	5	29	γ	γ	NOUN
ejpam-3759	5	30	-	-	PUNCT
ejpam-3759	5	31	ideals	ideal	NOUN
ejpam-3759	5	32	1	1	NUM
ejpam-3759	5	33	.	.	PUNCT
ejpam-3759	5	34	introduction	introduction	NOUN
ejpam-3759	5	35	and	and	CCONJ
ejpam-3759	5	36	preliminaries	preliminary	NOUN
ejpam-3759	5	37	ideal	ideal	ADJ
ejpam-3759	5	38	theory	theory	NOUN
ejpam-3759	5	39	in	in	ADP
ejpam-3759	5	40	semigroups	semigroup	NOUN
ejpam-3759	5	41	,	,	PUNCT
ejpam-3759	5	42	like	like	ADP
ejpam-3759	5	43	all	all	DET
ejpam-3759	5	44	other	other	ADJ
ejpam-3759	5	45	algebraic	algebraic	ADJ
ejpam-3759	5	46	structures	structure	NOUN
ejpam-3759	5	47	,	,	PUNCT
ejpam-3759	5	48	plays	play	VERB
ejpam-3759	5	49	an	an	DET
ejpam-3759	5	50	important	important	ADJ
ejpam-3759	5	51	role	role	NOUN
ejpam-3759	5	52	in	in	ADP
ejpam-3759	5	53	studying	study	VERB
ejpam-3759	5	54	them	they	PRON
ejpam-3759	5	55	.	.	PUNCT
ejpam-3759	6	1	good	good	ADJ
ejpam-3759	6	2	and	and	CCONJ
ejpam-3759	6	3	hughes	hughe	NOUN
ejpam-3759	7	1	[	[	X
ejpam-3759	7	2	8	8	NUM
ejpam-3759	7	3	]	]	PUNCT
ejpam-3759	7	4	introduced	introduce	VERB
ejpam-3759	7	5	the	the	DET
ejpam-3759	7	6	notion	notion	NOUN
ejpam-3759	7	7	of	of	ADP
ejpam-3759	7	8	bi	bi	NOUN
ejpam-3759	7	9	-	-	NOUN
ejpam-3759	7	10	ideals	ideal	NOUN
ejpam-3759	7	11	of	of	ADP
ejpam-3759	7	12	semigroups	semigroup	NOUN
ejpam-3759	7	13	in	in	ADP
ejpam-3759	7	14	1952	1952	NUM
ejpam-3759	7	15	.	.	PUNCT
ejpam-3759	8	1	an	an	DET
ejpam-3759	8	2	introductory	introductory	ADJ
ejpam-3759	8	3	definition	definition	NOUN
ejpam-3759	8	4	of	of	ADP
ejpam-3759	8	5	left	left	ADJ
ejpam-3759	8	6	,	,	PUNCT
ejpam-3759	8	7	right	right	INTJ
ejpam-3759	8	8	,	,	PUNCT
ejpam-3759	8	9	two	two	NUM
ejpam-3759	8	10	-	-	PUNCT
ejpam-3759	8	11	sided	side	VERB
ejpam-3759	8	12	almost	almost	ADV
ejpam-3759	8	13	ideals	ideal	NOUN
ejpam-3759	8	14	of	of	ADP
ejpam-3759	8	15	semigroups	semigroup	NOUN
ejpam-3759	8	16	was	be	AUX
ejpam-3759	8	17	launched	launch	VERB
ejpam-3759	8	18	by	by	ADP
ejpam-3759	8	19	grosek	grosek	NOUN
ejpam-3759	8	20	and	and	CCONJ
ejpam-3759	8	21	satko	satko	NOUN
ejpam-3759	9	1	[	[	X
ejpam-3759	9	2	9	9	NUM
ejpam-3759	9	3	]	]	PUNCT
ejpam-3759	9	4	in	in	ADP
ejpam-3759	9	5	1980	1980	NUM
ejpam-3759	9	6	.	.	PUNCT
ejpam-3759	10	1	they	they	PRON
ejpam-3759	10	2	gave	give	VERB
ejpam-3759	10	3	the	the	DET
ejpam-3759	10	4	characterization	characterization	NOUN
ejpam-3759	10	5	of	of	ADP
ejpam-3759	10	6	these	these	DET
ejpam-3759	10	7	ideals	ideal	NOUN
ejpam-3759	10	8	when	when	SCONJ
ejpam-3759	10	9	a	a	DET
ejpam-3759	10	10	semigroup	semigroup	NOUN
ejpam-3759	10	11	s	s	NOUN
ejpam-3759	10	12	contains	contain	VERB
ejpam-3759	10	13	no	no	DET
ejpam-3759	10	14	proper	proper	ADJ
ejpam-3759	10	15	left	left	NOUN
ejpam-3759	10	16	,	,	PUNCT
ejpam-3759	10	17	right	right	INTJ
ejpam-3759	10	18	,	,	PUNCT
ejpam-3759	10	19	two	two	NUM
ejpam-3759	10	20	-	-	PUNCT
ejpam-3759	10	21	sided	side	VERB
ejpam-3759	10	22	almost	almost	ADV
ejpam-3759	10	23	ideals	ideal	NOUN
ejpam-3759	10	24	in	in	ADP
ejpam-3759	10	25	[	[	X
ejpam-3759	10	26	9	9	NUM
ejpam-3759	10	27	]	]	PUNCT
ejpam-3759	10	28	,	,	PUNCT
ejpam-3759	10	29	and	and	CCONJ
ejpam-3759	10	30	afterwards	afterwards	ADV
ejpam-3759	10	31	,	,	PUNCT
ejpam-3759	10	32	they	they	PRON
ejpam-3759	10	33	discovered	discover	VERB
ejpam-3759	10	34	the	the	DET
ejpam-3759	10	35	minimal	minimal	ADJ
ejpam-3759	10	36	almost	almost	ADV
ejpam-3759	10	37	ideals	ideal	NOUN
ejpam-3759	10	38	and	and	CCONJ
ejpam-3759	10	39	the	the	DET
ejpam-3759	10	40	smallest	small	ADJ
ejpam-3759	10	41	almost	almost	ADV
ejpam-3759	10	42	ideals	ideal	NOUN
ejpam-3759	10	43	of	of	ADP
ejpam-3759	10	44	semigroups	semigroup	NOUN
ejpam-3759	10	45	in	in	ADP
ejpam-3759	10	46	[	[	X
ejpam-3759	10	47	10	10	NUM
ejpam-3759	10	48	]	]	PUNCT
ejpam-3759	10	49	and	and	CCONJ
ejpam-3759	10	50	[	[	X
ejpam-3759	10	51	11	11	NUM
ejpam-3759	10	52	]	]	PUNCT
ejpam-3759	10	53	,	,	PUNCT
ejpam-3759	10	54	respectively	respectively	ADV
ejpam-3759	10	55	.	.	PUNCT
ejpam-3759	11	1	in	in	ADP
ejpam-3759	11	2	1981	1981	NUM
ejpam-3759	11	3	,	,	PUNCT
ejpam-3759	11	4	bogdanovic	bogdanovic	ADJ
ejpam-3759	11	5	[	[	X
ejpam-3759	11	6	3	3	NUM
ejpam-3759	11	7	]	]	PUNCT
ejpam-3759	11	8	introduced	introduce	VERB
ejpam-3759	11	9	the	the	DET
ejpam-3759	11	10	definition	definition	NOUN
ejpam-3759	11	11	of	of	ADP
ejpam-3759	11	12	almost	almost	ADV
ejpam-3759	11	13	bi	bi	NOUN
ejpam-3759	11	14	-	-	NOUN
ejpam-3759	11	15	ideals	ideal	NOUN
ejpam-3759	11	16	in	in	ADP
ejpam-3759	11	17	semigroups	semigroup	NOUN
ejpam-3759	11	18	by	by	ADP
ejpam-3759	11	19	using	use	VERB
ejpam-3759	11	20	the	the	DET
ejpam-3759	11	21	definitions	definition	NOUN
ejpam-3759	11	22	of	of	ADP
ejpam-3759	11	23	almost	almost	ADV
ejpam-3759	11	24	ideals	ideal	NOUN
ejpam-3759	11	25	and	and	CCONJ
ejpam-3759	11	26	bi	bi	NOUN
ejpam-3759	11	27	-	-	NOUN
ejpam-3759	11	28	ideals	ideal	NOUN
ejpam-3759	11	29	in	in	ADP
ejpam-3759	11	30	semigroups	semigroup	NOUN
ejpam-3759	11	31	.	.	PUNCT
ejpam-3759	12	1	in	in	ADP
ejpam-3759	12	2	[	[	X
ejpam-3759	12	3	5	5	NUM
ejpam-3759	12	4	]	]	PUNCT
ejpam-3759	12	5	,	,	PUNCT
ejpam-3759	12	6	wattanatripop	wattanatripop	PROPN
ejpam-3759	12	7	,	,	PUNCT
ejpam-3759	12	8	chinram	chinram	PROPN
ejpam-3759	12	9	and	and	CCONJ
ejpam-3759	12	10	changphas	changphas	PROPN
ejpam-3759	12	11	gave	give	VERB
ejpam-3759	12	12	the	the	DET
ejpam-3759	12	13	properties	property	NOUN
ejpam-3759	12	14	of	of	ADP
ejpam-3759	12	15	quasialmost	quasialmost	NOUN
ejpam-3759	12	16	-	-	PUNCT
ejpam-3759	12	17	ideals	ideal	NOUN
ejpam-3759	12	18	and	and	CCONJ
ejpam-3759	12	19	first	first	ADV
ejpam-3759	12	20	defined	define	VERB
ejpam-3759	12	21	the	the	DET
ejpam-3759	12	22	concept	concept	NOUN
ejpam-3759	12	23	of	of	ADP
ejpam-3759	12	24	fuzzy	fuzzy	ADJ
ejpam-3759	12	25	almost	almost	ADV
ejpam-3759	12	26	ideals	ideal	NOUN
ejpam-3759	12	27	in	in	ADP
ejpam-3759	12	28	semigroups	semigroup	NOUN
ejpam-3759	12	29	.	.	PUNCT
ejpam-3759	13	1	moreover	moreover	ADV
ejpam-3759	13	2	,	,	PUNCT
ejpam-3759	13	3	they	they	PRON
ejpam-3759	13	4	provided	provide	VERB
ejpam-3759	13	5	the	the	DET
ejpam-3759	13	6	relationships	relationship	NOUN
ejpam-3759	13	7	between	between	ADP
ejpam-3759	13	8	almost	almost	ADV
ejpam-3759	13	9	ideals	ideal	NOUN
ejpam-3759	13	10	and	and	CCONJ
ejpam-3759	13	11	their	their	PRON
ejpam-3759	13	12	fuzzification	fuzzification	NOUN
ejpam-3759	13	13	.	.	PUNCT
ejpam-3759	14	1	furthermore	furthermore	ADV
ejpam-3759	14	2	,	,	PUNCT
ejpam-3759	14	3	they	they	PRON
ejpam-3759	14	4	investigated	investigate	VERB
ejpam-3759	14	5	fuzzification	fuzzification	NOUN
ejpam-3759	14	6	of	of	ADP
ejpam-3759	14	7	almost	almost	ADV
ejpam-3759	14	8	bi	bi	NOUN
ejpam-3759	14	9	-	-	NOUN
ejpam-3759	14	10	ideals	ideal	NOUN
ejpam-3759	14	11	in	in	ADP
ejpam-3759	14	12	semigroups	semigroup	NOUN
ejpam-3759	14	13	in	in	ADP
ejpam-3759	14	14	[	[	X
ejpam-3759	14	15	4	4	NUM
ejpam-3759	14	16	]	]	PUNCT
ejpam-3759	14	17	.	.	PUNCT
ejpam-3759	15	1	almost	almost	ADV
ejpam-3759	15	2	(	(	PUNCT
ejpam-3759	15	3	m	m	X
ejpam-3759	15	4	,	,	PUNCT
ejpam-3759	15	5	n)ideals	n)ideal	NOUN
ejpam-3759	15	6	and	and	CCONJ
ejpam-3759	15	7	their	their	PRON
ejpam-3759	15	8	fuzzification	fuzzification	NOUN
ejpam-3759	15	9	in	in	ADP
ejpam-3759	15	10	semigroups	semigroup	NOUN
ejpam-3759	15	11	were	be	AUX
ejpam-3759	15	12	studied	study	VERB
ejpam-3759	15	13	by	by	ADP
ejpam-3759	15	14	suebsung	suebsung	PROPN
ejpam-3759	15	15	,	,	PUNCT
ejpam-3759	15	16	wattanatripop	wattanatripop	NOUN
ejpam-3759	15	17	and	and	CCONJ
ejpam-3759	15	18	chinram	chinram	NOUN
ejpam-3759	15	19	in	in	ADP
ejpam-3759	15	20	[	[	X
ejpam-3759	15	21	23	23	NUM
ejpam-3759	15	22	]	]	PUNCT
ejpam-3759	15	23	.	.	PUNCT
ejpam-3759	16	1	moreover	moreover	ADV
ejpam-3759	16	2	,	,	PUNCT
ejpam-3759	16	3	the	the	DET
ejpam-3759	16	4	idea	idea	NOUN
ejpam-3759	16	5	of	of	ADP
ejpam-3759	16	6	almost	almost	ADV
ejpam-3759	16	7	ideals	ideal	NOUN
ejpam-3759	16	8	and	and	CCONJ
ejpam-3759	16	9	their	their	PRON
ejpam-3759	16	10	fuzzification	fuzzification	NOUN
ejpam-3759	16	11	were	be	AUX
ejpam-3759	16	12	extended	extend	VERB
ejpam-3759	16	13	to	to	ADP
ejpam-3759	16	14	n	n	CCONJ
ejpam-3759	16	15	-	-	PUNCT
ejpam-3759	16	16	ary	ary	PROPN
ejpam-3759	16	17	semigroups	semigroup	NOUN
ejpam-3759	16	18	in	in	ADP
ejpam-3759	16	19	[	[	X
ejpam-3759	16	20	21	21	NUM
ejpam-3759	16	21	]	]	PUNCT
ejpam-3759	16	22	.	.	PUNCT
ejpam-3759	17	1	∗corresponding	∗corresponde	VERB
ejpam-3759	17	2	author	author	NOUN
ejpam-3759	17	3	.	.	PUNCT
ejpam-3759	18	1	doi	doi	NOUN
ejpam-3759	18	2	:	:	PUNCT
ejpam-3759	18	3	https://doi.org/10.29020/nybg.ejpam.v13i3.3759	https://doi.org/10.29020/nybg.ejpam.v13i3.3759	PROPN
ejpam-3759	18	4	email	email	NOUN
ejpam-3759	18	5	addresses	address	NOUN
ejpam-3759	18	6	:	:	PUNCT
ejpam-3759	18	7	asimuen96@gmail.com	asimuen96@gmail.com	X
ejpam-3759	18	8	(	(	PUNCT
ejpam-3759	18	9	a.	a.	NOUN
ejpam-3759	18	10	simuen	simuen	PROPN
ejpam-3759	18	11	)	)	PUNCT
ejpam-3759	18	12	,	,	PUNCT
ejpam-3759	18	13	saleemabdullah@awkum.edu.pk	saleemabdullah@awkum.edu.pk	NOUN
ejpam-3759	18	14	(	(	PUNCT
ejpam-3759	18	15	s.	s.	PROPN
ejpam-3759	18	16	abdullah	abdullah	PROPN
ejpam-3759	18	17	)	)	PUNCT
ejpam-3759	18	18	,	,	PUNCT
ejpam-3759	18	19	winita.m@psu.ac.th	winita.m@psu.ac.th	PROPN
ejpam-3759	18	20	(	(	PUNCT
ejpam-3759	18	21	w.	w.	PROPN
ejpam-3759	18	22	yonthanthum	yonthanthum	PROPN
ejpam-3759	18	23	)	)	PUNCT
ejpam-3759	18	24	,	,	PUNCT
ejpam-3759	18	25	ronnason.c@psu.ac.th	ronnason.c@psu.ac.th	PROPN
ejpam-3759	18	26	(	(	PUNCT
ejpam-3759	18	27	r.	r.	PROPN
ejpam-3759	18	28	chinram	chinram	PROPN
ejpam-3759	18	29	)	)	PUNCT
ejpam-3759	18	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3759	19	1	620	620	NUM
ejpam-3759	20	1	c	c	NOUN
ejpam-3759	20	2	©	©	NOUN
ejpam-3759	20	3	2020	2020	NUM
ejpam-3759	20	4	ejpam	ejpam	VERB
ejpam-3759	20	5	all	all	DET
ejpam-3759	20	6	rights	right	NOUN
ejpam-3759	20	7	reserved	reserve	VERB
ejpam-3759	20	8	.	.	PUNCT
ejpam-3759	21	1	r.	r.	PROPN
ejpam-3759	21	2	chinram	chinram	PROPN
ejpam-3759	21	3	et	et	PROPN
ejpam-3759	21	4	al	al	PROPN
ejpam-3759	21	5	.	.	PUNCT
ejpam-3759	21	6	/	/	SYM
ejpam-3759	21	7	eur	eur	PROPN
ejpam-3759	21	8	.	.	PUNCT
ejpam-3759	22	1	j.	j.	PROPN
ejpam-3759	22	2	pure	pure	PROPN
ejpam-3759	22	3	appl	appl	PROPN
ejpam-3759	22	4	.	.	PROPN
ejpam-3759	22	5	math	math	PROPN
ejpam-3759	22	6	,	,	PUNCT
ejpam-3759	22	7	13	13	NUM
ejpam-3759	22	8	(	(	PUNCT
ejpam-3759	22	9	3	3	NUM
ejpam-3759	22	10	)	)	PUNCT
ejpam-3759	22	11	(	(	PUNCT
ejpam-3759	22	12	2020	2020	NUM
ejpam-3759	22	13	)	)	PUNCT
ejpam-3759	22	14	,	,	PUNCT
ejpam-3759	22	15	620	620	NUM
ejpam-3759	22	16	-	-	SYM
ejpam-3759	22	17	630	630	NUM
ejpam-3759	22	18	621	621	NUM
ejpam-3759	22	19	the	the	DET
ejpam-3759	22	20	notion	notion	NOUN
ejpam-3759	22	21	of	of	ADP
ejpam-3759	22	22	γ	γ	NOUN
ejpam-3759	22	23	-	-	PUNCT
ejpam-3759	22	24	semigroups	semigroup	NOUN
ejpam-3759	22	25	has	have	AUX
ejpam-3759	22	26	been	be	AUX
ejpam-3759	22	27	first	first	ADV
ejpam-3759	22	28	studied	study	VERB
ejpam-3759	22	29	by	by	ADP
ejpam-3759	22	30	sen	sen	PROPN
ejpam-3759	22	31	[	[	X
ejpam-3759	22	32	18	18	NUM
ejpam-3759	22	33	]	]	PUNCT
ejpam-3759	22	34	in	in	ADP
ejpam-3759	22	35	1981	1981	NUM
ejpam-3759	22	36	.	.	PUNCT
ejpam-3759	23	1	in	in	ADP
ejpam-3759	23	2	1986	1986	NUM
ejpam-3759	23	3	,	,	PUNCT
ejpam-3759	23	4	sen	sen	PROPN
ejpam-3759	23	5	and	and	CCONJ
ejpam-3759	23	6	saha	saha	PROPN
ejpam-3759	24	1	[	[	X
ejpam-3759	24	2	19	19	NUM
ejpam-3759	24	3	]	]	PUNCT
ejpam-3759	24	4	improved	improve	VERB
ejpam-3759	24	5	more	more	ADV
ejpam-3759	24	6	general	general	ADJ
ejpam-3759	24	7	definition	definition	NOUN
ejpam-3759	24	8	as	as	SCONJ
ejpam-3759	24	9	follows	follow	VERB
ejpam-3759	24	10	:	:	PUNCT
ejpam-3759	24	11	definition	definition	NOUN
ejpam-3759	24	12	1	1	NUM
ejpam-3759	24	13	.	.	PUNCT
ejpam-3759	25	1	(	(	PUNCT
ejpam-3759	25	2	[	[	X
ejpam-3759	25	3	19	19	NUM
ejpam-3759	25	4	]	]	PUNCT
ejpam-3759	25	5	)	)	PUNCT
ejpam-3759	25	6	let	let	VERB
ejpam-3759	25	7	m	m	PRON
ejpam-3759	25	8	and	and	CCONJ
ejpam-3759	25	9	γ	γ	PROPN
ejpam-3759	25	10	be	be	AUX
ejpam-3759	25	11	non	non	ADJ
ejpam-3759	25	12	-	-	ADJ
ejpam-3759	25	13	empty	empty	ADJ
ejpam-3759	25	14	sets	set	NOUN
ejpam-3759	25	15	.	.	PUNCT
ejpam-3759	26	1	(	(	PUNCT
ejpam-3759	26	2	m	m	PROPN
ejpam-3759	26	3	,	,	PUNCT
ejpam-3759	26	4	γ	γ	X
ejpam-3759	26	5	)	)	PUNCT
ejpam-3759	26	6	is	be	AUX
ejpam-3759	26	7	called	call	VERB
ejpam-3759	26	8	a	a	DET
ejpam-3759	26	9	γ	γ	NOUN
ejpam-3759	26	10	-	-	PUNCT
ejpam-3759	26	11	semigroup	semigroup	NOUN
ejpam-3759	26	12	if	if	SCONJ
ejpam-3759	26	13	it	it	PRON
ejpam-3759	26	14	satisfies	satisfy	VERB
ejpam-3759	26	15	the	the	DET
ejpam-3759	26	16	following	follow	VERB
ejpam-3759	26	17	laws	law	NOUN
ejpam-3759	26	18	.	.	PUNCT
ejpam-3759	27	1	(	(	PUNCT
ejpam-3759	27	2	1	1	X
ejpam-3759	27	3	)	)	PUNCT
ejpam-3759	27	4	aαb	aαb	NOUN
ejpam-3759	27	5	∈m	∈m	NOUN
ejpam-3759	27	6	for	for	ADP
ejpam-3759	27	7	all	all	DET
ejpam-3759	27	8	a	a	DET
ejpam-3759	27	9	,	,	PUNCT
ejpam-3759	27	10	b	b	NOUN
ejpam-3759	27	11	∈m	∈m	NOUN
ejpam-3759	27	12	and	and	CCONJ
ejpam-3759	27	13	α	α	PRON
ejpam-3759	27	14	∈	∈	PROPN
ejpam-3759	27	15	γ	γ	X
ejpam-3759	27	16	.	.	PROPN
ejpam-3759	28	1	(	(	PUNCT
ejpam-3759	28	2	2	2	X
ejpam-3759	28	3	)	)	PUNCT
ejpam-3759	28	4	m	m	VERB
ejpam-3759	28	5	is	be	AUX
ejpam-3759	28	6	associative	associative	ADJ
ejpam-3759	28	7	under	under	ADP
ejpam-3759	28	8	γ	γ	NOUN
ejpam-3759	28	9	,	,	PUNCT
ejpam-3759	28	10	that	that	ADV
ejpam-3759	28	11	is	is	ADV
ejpam-3759	28	12	(	(	PUNCT
ejpam-3759	28	13	aαb)βc	aαb)βc	ADJ
ejpam-3759	28	14	=	=	PUNCT
ejpam-3759	28	15	aα(bβc	aα(bβc	PROPN
ejpam-3759	28	16	)	)	PUNCT
ejpam-3759	28	17	for	for	ADP
ejpam-3759	28	18	all	all	DET
ejpam-3759	28	19	a	a	DET
ejpam-3759	28	20	,	,	PUNCT
ejpam-3759	28	21	b	b	NOUN
ejpam-3759	28	22	,	,	PUNCT
ejpam-3759	28	23	c	c	NOUN
ejpam-3759	28	24	∈m	∈m	NOUN
ejpam-3759	28	25	and	and	CCONJ
ejpam-3759	28	26	all	all	DET
ejpam-3759	28	27	α	α	NOUN
ejpam-3759	28	28	,	,	PUNCT
ejpam-3759	28	29	β	β	PROPN
ejpam-3759	28	30	∈	∈	PROPN
ejpam-3759	28	31	γ	γ	X
ejpam-3759	28	32	.	.	PUNCT
ejpam-3759	29	1	every	every	DET
ejpam-3759	29	2	semigroup	semigroup	NOUN
ejpam-3759	29	3	(	(	PUNCT
ejpam-3759	29	4	s	s	PROPN
ejpam-3759	29	5	,	,	PUNCT
ejpam-3759	29	6	·	·	PUNCT
ejpam-3759	29	7	)	)	PUNCT
ejpam-3759	29	8	can	can	AUX
ejpam-3759	29	9	be	be	AUX
ejpam-3759	29	10	considered	consider	VERB
ejpam-3759	29	11	as	as	ADP
ejpam-3759	29	12	a	a	DET
ejpam-3759	29	13	γ	γ	NOUN
ejpam-3759	29	14	-	-	PUNCT
ejpam-3759	29	15	semigroup	semigroup	NOUN
ejpam-3759	29	16	s	s	NOUN
ejpam-3759	29	17	by	by	ADP
ejpam-3759	29	18	choosing	choose	VERB
ejpam-3759	29	19	γ	γ	X
ejpam-3759	29	20	=	=	PUNCT
ejpam-3759	29	21	{	{	PUNCT
ejpam-3759	29	22	·	·	PUNCT
ejpam-3759	29	23	}	}	PUNCT
ejpam-3759	29	24	.	.	PUNCT
ejpam-3759	30	1	then	then	ADV
ejpam-3759	30	2	a	a	DET
ejpam-3759	30	3	γ	γ	PROPN
ejpam-3759	30	4	-	-	PUNCT
ejpam-3759	30	5	semigroup	semigroup	NOUN
ejpam-3759	30	6	is	be	AUX
ejpam-3759	30	7	one	one	NUM
ejpam-3759	30	8	of	of	ADP
ejpam-3759	30	9	the	the	DET
ejpam-3759	30	10	generalizations	generalization	NOUN
ejpam-3759	30	11	of	of	ADP
ejpam-3759	30	12	semigroups	semigroup	NOUN
ejpam-3759	30	13	.	.	PUNCT
ejpam-3759	31	1	the	the	DET
ejpam-3759	31	2	investigation	investigation	NOUN
ejpam-3759	31	3	on	on	ADP
ejpam-3759	31	4	γ	γ	NOUN
ejpam-3759	31	5	-	-	PUNCT
ejpam-3759	31	6	semigroups	semigroup	NOUN
ejpam-3759	31	7	was	be	AUX
ejpam-3759	31	8	done	do	VERB
ejpam-3759	31	9	by	by	ADP
ejpam-3759	31	10	certain	certain	ADJ
ejpam-3759	31	11	mathematicians	mathematician	NOUN
ejpam-3759	31	12	which	which	PRON
ejpam-3759	31	13	are	be	AUX
ejpam-3759	31	14	parallel	parallel	ADJ
ejpam-3759	31	15	to	to	ADP
ejpam-3759	31	16	some	some	DET
ejpam-3759	31	17	results	result	NOUN
ejpam-3759	31	18	of	of	ADP
ejpam-3759	31	19	semigroups	semigroup	NOUN
ejpam-3759	31	20	,	,	PUNCT
ejpam-3759	31	21	for	for	ADP
ejpam-3759	31	22	example	example	NOUN
ejpam-3759	31	23	,	,	PUNCT
ejpam-3759	31	24	one	one	PRON
ejpam-3759	31	25	may	may	AUX
ejpam-3759	31	26	see	see	VERB
ejpam-3759	31	27	[	[	X
ejpam-3759	31	28	6	6	NUM
ejpam-3759	31	29	,	,	PUNCT
ejpam-3759	31	30	7	7	NUM
ejpam-3759	31	31	,	,	PUNCT
ejpam-3759	31	32	17–19	17–19	NUM
ejpam-3759	31	33	]	]	PUNCT
ejpam-3759	31	34	.	.	PUNCT
ejpam-3759	32	1	similar	similar	ADJ
ejpam-3759	32	2	to	to	ADP
ejpam-3759	32	3	semigroups	semigroup	NOUN
ejpam-3759	32	4	,	,	PUNCT
ejpam-3759	32	5	ideal	ideal	ADJ
ejpam-3759	32	6	theory	theory	NOUN
ejpam-3759	32	7	in	in	ADP
ejpam-3759	32	8	γ	γ	NOUN
ejpam-3759	32	9	-	-	PUNCT
ejpam-3759	32	10	semigroups	semigroup	NOUN
ejpam-3759	32	11	plays	play	VERB
ejpam-3759	32	12	an	an	DET
ejpam-3759	32	13	important	important	ADJ
ejpam-3759	32	14	role	role	NOUN
ejpam-3759	32	15	(	(	PUNCT
ejpam-3759	32	16	for	for	ADP
ejpam-3759	32	17	example	example	NOUN
ejpam-3759	32	18	,	,	PUNCT
ejpam-3759	32	19	we	we	PRON
ejpam-3759	32	20	can	can	AUX
ejpam-3759	32	21	see	see	VERB
ejpam-3759	32	22	in	in	ADP
ejpam-3759	32	23	[	[	X
ejpam-3759	32	24	1	1	NUM
ejpam-3759	32	25	,	,	PUNCT
ejpam-3759	32	26	6	6	NUM
ejpam-3759	32	27	,	,	PUNCT
ejpam-3759	32	28	7	7	NUM
ejpam-3759	32	29	,	,	PUNCT
ejpam-3759	32	30	12–14	12–14	NUM
ejpam-3759	32	31	,	,	PUNCT
ejpam-3759	32	32	20	20	NUM
ejpam-3759	32	33	]	]	PUNCT
ejpam-3759	32	34	)	)	PUNCT
ejpam-3759	32	35	.	.	PUNCT
ejpam-3759	33	1	let	let	VERB
ejpam-3759	33	2	m	m	PRON
ejpam-3759	33	3	be	be	AUX
ejpam-3759	33	4	a	a	DET
ejpam-3759	33	5	γ	γ	NOUN
ejpam-3759	33	6	-	-	PUNCT
ejpam-3759	33	7	semigroup	semigroup	NOUN
ejpam-3759	33	8	.	.	PUNCT
ejpam-3759	34	1	for	for	ADP
ejpam-3759	34	2	nonempty	nonempty	NOUN
ejpam-3759	34	3	subsets	subset	NOUN
ejpam-3759	34	4	a	a	PRON
ejpam-3759	34	5	and	and	CCONJ
ejpam-3759	34	6	b	b	NOUN
ejpam-3759	34	7	of	of	ADP
ejpam-3759	34	8	m	m	PRON
ejpam-3759	34	9	,	,	PUNCT
ejpam-3759	34	10	let	let	VERB
ejpam-3759	34	11	aγb	aγb	NOUN
ejpam-3759	34	12	=	=	PRON
ejpam-3759	34	13	{	{	PUNCT
ejpam-3759	34	14	aαb	aαb	NOUN
ejpam-3759	34	15	|	|	ADV
ejpam-3759	34	16	a	a	DET
ejpam-3759	34	17	∈	∈	PROPN
ejpam-3759	34	18	a	a	PRON
ejpam-3759	34	19	,	,	PUNCT
ejpam-3759	34	20	b	b	PROPN
ejpam-3759	34	21	∈	∈	PROPN
ejpam-3759	34	22	b	b	PROPN
ejpam-3759	34	23	,	,	PUNCT
ejpam-3759	34	24	α	α	PROPN
ejpam-3759	34	25	∈	∈	PROPN
ejpam-3759	34	26	γ	γ	X
ejpam-3759	34	27	}	}	PUNCT
ejpam-3759	34	28	.	.	PUNCT
ejpam-3759	35	1	if	if	SCONJ
ejpam-3759	35	2	m	m	PROPN
ejpam-3759	35	3	∈m	∈m	VERB
ejpam-3759	35	4	,	,	PUNCT
ejpam-3759	35	5	we	we	PRON
ejpam-3759	35	6	let	let	VERB
ejpam-3759	35	7	aγm	aγm	NOUN
ejpam-3759	35	8	=	=	SYM
ejpam-3759	35	9	aγ{m	aγ{m	PROPN
ejpam-3759	35	10	}	}	PUNCT
ejpam-3759	35	11	and	and	CCONJ
ejpam-3759	35	12	mγa	mγa	PROPN
ejpam-3759	35	13	=	=	SYM
ejpam-3759	35	14	{	{	PUNCT
ejpam-3759	35	15	m}γa	m}γa	NOUN
ejpam-3759	35	16	.	.	PUNCT
ejpam-3759	36	1	if	if	SCONJ
ejpam-3759	36	2	α	α	PROPN
ejpam-3759	36	3	∈	∈	PROPN
ejpam-3759	36	4	γ	γ	X
ejpam-3759	36	5	,	,	PUNCT
ejpam-3759	36	6	we	we	PRON
ejpam-3759	36	7	let	let	VERB
ejpam-3759	36	8	aαb	aαb	NOUN
ejpam-3759	36	9	=	=	PRON
ejpam-3759	36	10	{	{	PUNCT
ejpam-3759	36	11	aαb	aαb	NOUN
ejpam-3759	36	12	|	|	ADV
ejpam-3759	36	13	a	a	DET
ejpam-3759	36	14	∈	∈	PROPN
ejpam-3759	36	15	a	a	PRON
ejpam-3759	36	16	,	,	PUNCT
ejpam-3759	36	17	b	b	PROPN
ejpam-3759	36	18	∈	∈	PROPN
ejpam-3759	36	19	b	b	NOUN
ejpam-3759	36	20	}	}	PUNCT
ejpam-3759	36	21	.	.	PUNCT
ejpam-3759	37	1	definition	definition	NOUN
ejpam-3759	37	2	2	2	NUM
ejpam-3759	37	3	.	.	PUNCT
ejpam-3759	38	1	(	(	PUNCT
ejpam-3759	38	2	see	see	VERB
ejpam-3759	38	3	[	[	X
ejpam-3759	38	4	7	7	NUM
ejpam-3759	38	5	]	]	PUNCT
ejpam-3759	38	6	)	)	PUNCT
ejpam-3759	38	7	let	let	VERB
ejpam-3759	38	8	m	m	PRON
ejpam-3759	38	9	be	be	AUX
ejpam-3759	38	10	a	a	DET
ejpam-3759	38	11	γ	γ	NOUN
ejpam-3759	38	12	-	-	PUNCT
ejpam-3759	38	13	semigroup	semigroup	NOUN
ejpam-3759	38	14	.	.	PUNCT
ejpam-3759	39	1	(	(	PUNCT
ejpam-3759	39	2	1	1	X
ejpam-3759	39	3	)	)	PUNCT
ejpam-3759	39	4	a	a	DET
ejpam-3759	39	5	nonempty	nonempty	NOUN
ejpam-3759	39	6	subset	subset	VERB
ejpam-3759	39	7	t	t	PROPN
ejpam-3759	39	8	of	of	ADP
ejpam-3759	39	9	m	m	PROPN
ejpam-3759	39	10	is	be	AUX
ejpam-3759	39	11	called	call	VERB
ejpam-3759	39	12	a	a	DET
ejpam-3759	39	13	sub	sub	NOUN
ejpam-3759	39	14	γ	γ	NOUN
ejpam-3759	39	15	-	-	PUNCT
ejpam-3759	39	16	semigroup	semigroup	NOUN
ejpam-3759	39	17	of	of	ADP
ejpam-3759	39	18	m	m	PRON
ejpam-3759	39	19	if	if	SCONJ
ejpam-3759	39	20	tγt	tγt	NOUN
ejpam-3759	39	21	⊆	⊆	NUM
ejpam-3759	39	22	t	t	NOUN
ejpam-3759	39	23	.	.	PUNCT
ejpam-3759	40	1	(	(	PUNCT
ejpam-3759	40	2	2	2	X
ejpam-3759	40	3	)	)	PUNCT
ejpam-3759	40	4	a	a	DET
ejpam-3759	40	5	sub	sub	NOUN
ejpam-3759	40	6	γ	γ	X
ejpam-3759	40	7	-	-	PUNCT
ejpam-3759	40	8	semigroup	semigroup	PROPN
ejpam-3759	40	9	b	b	PROPN
ejpam-3759	40	10	of	of	ADP
ejpam-3759	40	11	m	m	PROPN
ejpam-3759	40	12	is	be	AUX
ejpam-3759	40	13	called	call	VERB
ejpam-3759	40	14	a	a	DET
ejpam-3759	40	15	bi	bi	ADJ
ejpam-3759	40	16	-	-	ADJ
ejpam-3759	40	17	γ	γ	NOUN
ejpam-3759	40	18	-	-	NOUN
ejpam-3759	40	19	ideal	ideal	NOUN
ejpam-3759	40	20	of	of	ADP
ejpam-3759	40	21	m	m	PRON
ejpam-3759	40	22	if	if	SCONJ
ejpam-3759	40	23	bγmγb	bγmγb	VERB
ejpam-3759	40	24	⊆	⊆	NUM
ejpam-3759	40	25	b.	b.	PROPN
ejpam-3759	40	26	a	a	DET
ejpam-3759	40	27	bi	bi	PROPN
ejpam-3759	40	28	-	-	ADJ
ejpam-3759	40	29	γ	γ	NOUN
ejpam-3759	40	30	-	-	NOUN
ejpam-3759	40	31	ideal	ideal	NOUN
ejpam-3759	40	32	in	in	ADP
ejpam-3759	40	33	γ	γ	NOUN
ejpam-3759	40	34	-	-	PUNCT
ejpam-3759	40	35	semigroups	semigroup	NOUN
ejpam-3759	40	36	was	be	AUX
ejpam-3759	40	37	sometimes	sometimes	ADV
ejpam-3759	40	38	called	call	VERB
ejpam-3759	40	39	a	a	DET
ejpam-3759	40	40	bi	bi	NOUN
ejpam-3759	40	41	-	-	NOUN
ejpam-3759	40	42	ideal	ideal	ADJ
ejpam-3759	40	43	(	(	PUNCT
ejpam-3759	40	44	see	see	VERB
ejpam-3759	40	45	[	[	X
ejpam-3759	40	46	14	14	NUM
ejpam-3759	40	47	]	]	NUM
ejpam-3759	40	48	)	)	PUNCT
ejpam-3759	40	49	.	.	PUNCT
ejpam-3759	41	1	some	some	DET
ejpam-3759	41	2	generalizations	generalization	NOUN
ejpam-3759	41	3	of	of	ADP
ejpam-3759	41	4	this	this	DET
ejpam-3759	41	5	ideal	ideal	NOUN
ejpam-3759	41	6	were	be	AUX
ejpam-3759	41	7	studied	study	VERB
ejpam-3759	41	8	in	in	ADP
ejpam-3759	41	9	[	[	X
ejpam-3759	41	10	2	2	NUM
ejpam-3759	41	11	]	]	PUNCT
ejpam-3759	41	12	and	and	CCONJ
ejpam-3759	41	13	[	[	X
ejpam-3759	41	14	16	16	NUM
ejpam-3759	41	15	]	]	PUNCT
ejpam-3759	41	16	.	.	PUNCT
ejpam-3759	42	1	recently	recently	ADV
ejpam-3759	42	2	,	,	PUNCT
ejpam-3759	42	3	wattanatripop	wattanatripop	PROPN
ejpam-3759	42	4	and	and	CCONJ
ejpam-3759	42	5	changphas	changphas	PROPN
ejpam-3759	42	6	first	first	ADV
ejpam-3759	42	7	studied	study	VERB
ejpam-3759	42	8	the	the	DET
ejpam-3759	42	9	concept	concept	NOUN
ejpam-3759	42	10	of	of	ADP
ejpam-3759	42	11	almost	almost	ADV
ejpam-3759	42	12	ideals	ideal	NOUN
ejpam-3759	42	13	in	in	ADP
ejpam-3759	42	14	γ	γ	NOUN
ejpam-3759	42	15	-	-	PUNCT
ejpam-3759	42	16	semigroups	semigroup	NOUN
ejpam-3759	42	17	.	.	PUNCT
ejpam-3759	43	1	in	in	ADP
ejpam-3759	43	2	[	[	X
ejpam-3759	43	3	22	22	NUM
ejpam-3759	43	4	]	]	PUNCT
ejpam-3759	43	5	,	,	PUNCT
ejpam-3759	43	6	they	they	PRON
ejpam-3759	43	7	defined	define	VERB
ejpam-3759	43	8	the	the	DET
ejpam-3759	43	9	definitions	definition	NOUN
ejpam-3759	43	10	of	of	ADP
ejpam-3759	43	11	left	left	NOUN
ejpam-3759	43	12	[	[	X
ejpam-3759	43	13	right	right	X
ejpam-3759	43	14	]	]	X
ejpam-3759	43	15	almost	almost	ADV
ejpam-3759	43	16	ideals	ideal	NOUN
ejpam-3759	43	17	in	in	ADP
ejpam-3759	43	18	γ	γ	NOUN
ejpam-3759	43	19	-	-	PUNCT
ejpam-3759	43	20	semigroups	semigroup	NOUN
ejpam-3759	43	21	.	.	PUNCT
ejpam-3759	44	1	moreover	moreover	ADV
ejpam-3759	44	2	,	,	PUNCT
ejpam-3759	44	3	a	a	DET
ejpam-3759	44	4	γ	γ	PROPN
ejpam-3759	44	5	-	-	PUNCT
ejpam-3759	44	6	semigroup	semigroup	NOUN
ejpam-3759	44	7	containing	contain	VERB
ejpam-3759	44	8	no	no	DET
ejpam-3759	44	9	proper	proper	ADJ
ejpam-3759	44	10	left	left	NOUN
ejpam-3759	44	11	[	[	X
ejpam-3759	44	12	right	right	X
ejpam-3759	44	13	]	]	PUNCT
ejpam-3759	44	14	almost	almost	ADV
ejpam-3759	44	15	ideals	ideal	NOUN
ejpam-3759	44	16	was	be	AUX
ejpam-3759	44	17	characterized	characterize	VERB
ejpam-3759	44	18	.	.	PUNCT
ejpam-3759	45	1	in	in	ADP
ejpam-3759	45	2	1965	1965	NUM
ejpam-3759	45	3	,	,	PUNCT
ejpam-3759	45	4	zadeh	zadeh	PROPN
ejpam-3759	45	5	[	[	X
ejpam-3759	45	6	24	24	NUM
ejpam-3759	45	7	]	]	PUNCT
ejpam-3759	45	8	introduced	introduce	VERB
ejpam-3759	45	9	the	the	DET
ejpam-3759	45	10	concept	concept	NOUN
ejpam-3759	45	11	of	of	ADP
ejpam-3759	45	12	fundamental	fundamental	ADJ
ejpam-3759	45	13	fuzzy	fuzzy	ADJ
ejpam-3759	45	14	sets	set	NOUN
ejpam-3759	45	15	.	.	PUNCT
ejpam-3759	46	1	since	since	SCONJ
ejpam-3759	46	2	then	then	ADV
ejpam-3759	46	3	,	,	PUNCT
ejpam-3759	46	4	fuzzy	fuzzy	ADJ
ejpam-3759	46	5	sets	set	NOUN
ejpam-3759	46	6	have	have	AUX
ejpam-3759	46	7	been	be	AUX
ejpam-3759	46	8	studied	study	VERB
ejpam-3759	46	9	in	in	ADP
ejpam-3759	46	10	various	various	ADJ
ejpam-3759	46	11	fields	field	NOUN
ejpam-3759	46	12	.	.	PUNCT
ejpam-3759	47	1	a	a	DET
ejpam-3759	47	2	function	function	NOUN
ejpam-3759	47	3	from	from	ADP
ejpam-3759	47	4	a	a	DET
ejpam-3759	47	5	set	set	NOUN
ejpam-3759	47	6	m	m	NOUN
ejpam-3759	47	7	into	into	ADP
ejpam-3759	47	8	the	the	DET
ejpam-3759	47	9	closed	closed	ADJ
ejpam-3759	47	10	unit	unit	NOUN
ejpam-3759	47	11	interval	interval	NOUN
ejpam-3759	47	12	[	[	X
ejpam-3759	47	13	0	0	NUM
ejpam-3759	47	14	,	,	PUNCT
ejpam-3759	47	15	1	1	NUM
ejpam-3759	47	16	]	]	PUNCT
ejpam-3759	47	17	is	be	AUX
ejpam-3759	47	18	called	call	VERB
ejpam-3759	47	19	a	a	DET
ejpam-3759	47	20	fuzzy	fuzzy	ADJ
ejpam-3759	47	21	subset	subset	NOUN
ejpam-3759	47	22	of	of	ADP
ejpam-3759	47	23	m	m	PROPN
ejpam-3759	47	24	.	.	PUNCT
ejpam-3759	48	1	let	let	VERB
ejpam-3759	48	2	f	f	PROPN
ejpam-3759	48	3	and	and	CCONJ
ejpam-3759	48	4	g	g	PROPN
ejpam-3759	48	5	be	be	VERB
ejpam-3759	48	6	any	any	DET
ejpam-3759	48	7	two	two	NUM
ejpam-3759	48	8	fuzzy	fuzzy	ADJ
ejpam-3759	48	9	subsets	subset	NOUN
ejpam-3759	48	10	of	of	ADP
ejpam-3759	48	11	a	a	DET
ejpam-3759	48	12	set	set	NOUN
ejpam-3759	48	13	m	m	NOUN
ejpam-3759	48	14	.	.	PUNCT
ejpam-3759	49	1	(	(	PUNCT
ejpam-3759	49	2	1	1	X
ejpam-3759	49	3	)	)	PUNCT
ejpam-3759	49	4	a	a	DET
ejpam-3759	49	5	fuzzy	fuzzy	ADJ
ejpam-3759	49	6	subset	subset	NOUN
ejpam-3759	49	7	f	f	PROPN
ejpam-3759	49	8	∩	∩	PROPN
ejpam-3759	49	9	g	g	PROPN
ejpam-3759	49	10	of	of	ADP
ejpam-3759	49	11	m	m	PROPN
ejpam-3759	49	12	is	be	AUX
ejpam-3759	49	13	defined	define	VERB
ejpam-3759	49	14	by	by	ADP
ejpam-3759	49	15	(	(	PUNCT
ejpam-3759	49	16	f	f	PROPN
ejpam-3759	49	17	∩	∩	ADJ
ejpam-3759	49	18	g)(m	g)(m	X
ejpam-3759	49	19	)	)	PUNCT
ejpam-3759	49	20	=	=	SYM
ejpam-3759	49	21	min{f(m	min{f(m	PROPN
ejpam-3759	49	22	)	)	PUNCT
ejpam-3759	49	23	,	,	PUNCT
ejpam-3759	49	24	g(m	g(m	VERB
ejpam-3759	49	25	)	)	PUNCT
ejpam-3759	49	26	}	}	PUNCT
ejpam-3759	49	27	for	for	ADP
ejpam-3759	49	28	all	all	DET
ejpam-3759	49	29	m	m	NOUN
ejpam-3759	49	30	∈m	∈m	NOUN
ejpam-3759	49	31	.	.	PUNCT
ejpam-3759	50	1	r.	r.	PROPN
ejpam-3759	50	2	chinram	chinram	PROPN
ejpam-3759	50	3	et	et	PROPN
ejpam-3759	50	4	al	al	PROPN
ejpam-3759	50	5	.	.	PUNCT
ejpam-3759	50	6	/	/	SYM
ejpam-3759	50	7	eur	eur	PROPN
ejpam-3759	50	8	.	.	PUNCT
ejpam-3759	51	1	j.	j.	PROPN
ejpam-3759	51	2	pure	pure	PROPN
ejpam-3759	51	3	appl	appl	PROPN
ejpam-3759	51	4	.	.	PROPN
ejpam-3759	51	5	math	math	PROPN
ejpam-3759	51	6	,	,	PUNCT
ejpam-3759	51	7	13	13	NUM
ejpam-3759	51	8	(	(	PUNCT
ejpam-3759	51	9	3	3	NUM
ejpam-3759	51	10	)	)	PUNCT
ejpam-3759	51	11	(	(	PUNCT
ejpam-3759	51	12	2020	2020	NUM
ejpam-3759	51	13	)	)	PUNCT
ejpam-3759	51	14	,	,	PUNCT
ejpam-3759	51	15	620	620	NUM
ejpam-3759	51	16	-	-	SYM
ejpam-3759	51	17	630	630	NUM
ejpam-3759	51	18	622	622	NUM
ejpam-3759	51	19	(	(	PUNCT
ejpam-3759	51	20	2	2	NUM
ejpam-3759	51	21	)	)	PUNCT
ejpam-3759	51	22	a	a	DET
ejpam-3759	51	23	fuzzy	fuzzy	ADJ
ejpam-3759	51	24	subset	subset	NOUN
ejpam-3759	52	1	f	f	PROPN
ejpam-3759	52	2	∪	∪	ADP
ejpam-3759	52	3	g	g	PROPN
ejpam-3759	52	4	of	of	ADP
ejpam-3759	52	5	m	m	PROPN
ejpam-3759	52	6	is	be	AUX
ejpam-3759	52	7	defined	define	VERB
ejpam-3759	52	8	by	by	ADP
ejpam-3759	52	9	(	(	PUNCT
ejpam-3759	52	10	f	f	PROPN
ejpam-3759	52	11	∪	∪	ADP
ejpam-3759	52	12	g)(m	g)(m	PROPN
ejpam-3759	52	13	)	)	PUNCT
ejpam-3759	52	14	=	=	SYM
ejpam-3759	52	15	max{f(m	max{f(m	PROPN
ejpam-3759	52	16	)	)	PUNCT
ejpam-3759	52	17	,	,	PUNCT
ejpam-3759	52	18	g(m	g(m	VERB
ejpam-3759	52	19	)	)	PUNCT
ejpam-3759	52	20	}	}	PUNCT
ejpam-3759	52	21	for	for	ADP
ejpam-3759	52	22	all	all	DET
ejpam-3759	52	23	m	m	NOUN
ejpam-3759	52	24	∈m	∈m	NOUN
ejpam-3759	52	25	.	.	PUNCT
ejpam-3759	53	1	(	(	PUNCT
ejpam-3759	53	2	3	3	X
ejpam-3759	53	3	)	)	PUNCT
ejpam-3759	53	4	if	if	SCONJ
ejpam-3759	53	5	f(m	f(m	PROPN
ejpam-3759	53	6	)	)	PUNCT
ejpam-3759	53	7	≤	≤	NOUN
ejpam-3759	53	8	g(m	g(m	VERB
ejpam-3759	53	9	)	)	PUNCT
ejpam-3759	53	10	for	for	ADP
ejpam-3759	53	11	all	all	DET
ejpam-3759	53	12	m	m	NOUN
ejpam-3759	53	13	∈m	∈m	NOUN
ejpam-3759	53	14	,	,	PUNCT
ejpam-3759	53	15	we	we	PRON
ejpam-3759	53	16	say	say	VERB
ejpam-3759	53	17	that	that	SCONJ
ejpam-3759	53	18	f	f	PROPN
ejpam-3759	53	19	is	be	AUX
ejpam-3759	53	20	a	a	DET
ejpam-3759	53	21	subset	subset	NOUN
ejpam-3759	53	22	of	of	ADP
ejpam-3759	53	23	g	g	NOUN
ejpam-3759	53	24	,	,	PUNCT
ejpam-3759	53	25	and	and	CCONJ
ejpam-3759	53	26	use	use	VERB
ejpam-3759	53	27	the	the	DET
ejpam-3759	53	28	notation	notation	NOUN
ejpam-3759	53	29	f	f	PROPN
ejpam-3759	53	30	⊆	⊆	NUM
ejpam-3759	53	31	g	g	NOUN
ejpam-3759	53	32	and	and	CCONJ
ejpam-3759	53	33	sometimes	sometimes	ADV
ejpam-3759	53	34	we	we	PRON
ejpam-3759	53	35	will	will	AUX
ejpam-3759	53	36	say	say	VERB
ejpam-3759	53	37	that	that	SCONJ
ejpam-3759	53	38	f	f	PROPN
ejpam-3759	53	39	is	be	AUX
ejpam-3759	53	40	contained	contain	VERB
ejpam-3759	53	41	in	in	ADP
ejpam-3759	53	42	g.	g.	PROPN
ejpam-3759	53	43	for	for	ADP
ejpam-3759	53	44	a	a	DET
ejpam-3759	53	45	fuzzy	fuzzy	ADJ
ejpam-3759	53	46	subset	subset	NOUN
ejpam-3759	53	47	f	f	PROPN
ejpam-3759	53	48	of	of	ADP
ejpam-3759	53	49	any	any	DET
ejpam-3759	53	50	set	set	NOUN
ejpam-3759	53	51	m	m	VERB
ejpam-3759	53	52	,	,	PUNCT
ejpam-3759	53	53	the	the	DET
ejpam-3759	53	54	support	support	NOUN
ejpam-3759	53	55	of	of	ADP
ejpam-3759	53	56	f	f	PROPN
ejpam-3759	53	57	is	be	AUX
ejpam-3759	53	58	the	the	DET
ejpam-3759	53	59	set	set	NOUN
ejpam-3759	53	60	of	of	ADP
ejpam-3759	53	61	points	point	NOUN
ejpam-3759	53	62	in	in	ADP
ejpam-3759	53	63	m	m	PROPN
ejpam-3759	53	64	defined	define	VERB
ejpam-3759	53	65	by	by	ADP
ejpam-3759	53	66	supp(f	supp(f	PROPN
ejpam-3759	53	67	)	)	PUNCT
ejpam-3759	53	68	=	=	PRON
ejpam-3759	53	69	{	{	PUNCT
ejpam-3759	53	70	m	m	NOUN
ejpam-3759	53	71	∈m	∈m	NOUN
ejpam-3759	53	72	|	|	ADV
ejpam-3759	53	73	f(m	f(m	NOUN
ejpam-3759	53	74	)	)	PUNCT
ejpam-3759	53	75	6=	6=	ADP
ejpam-3759	53	76	0	0	NUM
ejpam-3759	53	77	}	}	PUNCT
ejpam-3759	53	78	.	.	PUNCT
ejpam-3759	54	1	for	for	ADP
ejpam-3759	54	2	a	a	DET
ejpam-3759	54	3	subset	subset	NOUN
ejpam-3759	54	4	a	a	PRON
ejpam-3759	54	5	of	of	ADP
ejpam-3759	54	6	any	any	DET
ejpam-3759	54	7	set	set	NOUN
ejpam-3759	54	8	m	m	VERB
ejpam-3759	54	9	,	,	PUNCT
ejpam-3759	54	10	the	the	DET
ejpam-3759	54	11	characteristic	characteristic	ADJ
ejpam-3759	54	12	function	function	NOUN
ejpam-3759	54	13	χa	χa	NOUN
ejpam-3759	54	14	of	of	ADP
ejpam-3759	54	15	a	a	PRON
ejpam-3759	54	16	is	be	AUX
ejpam-3759	54	17	a	a	DET
ejpam-3759	54	18	fuzzy	fuzzy	ADJ
ejpam-3759	54	19	subset	subset	NOUN
ejpam-3759	54	20	of	of	ADP
ejpam-3759	54	21	m	m	AUX
ejpam-3759	54	22	defined	define	VERB
ejpam-3759	54	23	by	by	ADP
ejpam-3759	54	24	χa(m	χa(m	NOUN
ejpam-3759	54	25	)	)	PUNCT
ejpam-3759	55	1	=	=	SYM
ejpam-3759	55	2	{	{	PUNCT
ejpam-3759	55	3	1	1	NUM
ejpam-3759	55	4	m	m	NOUN
ejpam-3759	55	5	∈	∈	PROPN
ejpam-3759	55	6	a	a	PRON
ejpam-3759	55	7	,	,	PUNCT
ejpam-3759	55	8	0	0	NUM
ejpam-3759	55	9	m	m	NOUN
ejpam-3759	55	10	/∈	/∈	NOUN
ejpam-3759	55	11	a.	a.	NOUN
ejpam-3759	55	12	for	for	ADP
ejpam-3759	55	13	any	any	DET
ejpam-3759	55	14	element	element	NOUN
ejpam-3759	55	15	m	m	NOUN
ejpam-3759	55	16	of	of	ADP
ejpam-3759	55	17	any	any	DET
ejpam-3759	55	18	set	set	NOUN
ejpam-3759	55	19	m	m	PROPN
ejpam-3759	55	20	and	and	CCONJ
ejpam-3759	55	21	t	t	PROPN
ejpam-3759	55	22	∈	∈	PROPN
ejpam-3759	55	23	(	(	PUNCT
ejpam-3759	55	24	0	0	NUM
ejpam-3759	55	25	,	,	PUNCT
ejpam-3759	55	26	1	1	NUM
ejpam-3759	55	27	]	]	PUNCT
ejpam-3759	55	28	,	,	PUNCT
ejpam-3759	55	29	a	a	DET
ejpam-3759	55	30	fuzzy	fuzzy	ADJ
ejpam-3759	55	31	point	point	NOUN
ejpam-3759	55	32	mt	mt	PROPN
ejpam-3759	55	33	of	of	ADP
ejpam-3759	55	34	m	m	PROPN
ejpam-3759	55	35	is	be	AUX
ejpam-3759	55	36	a	a	DET
ejpam-3759	55	37	fuzzy	fuzzy	ADJ
ejpam-3759	55	38	subset	subset	NOUN
ejpam-3759	55	39	of	of	ADP
ejpam-3759	55	40	m	m	AUX
ejpam-3759	55	41	defined	define	VERB
ejpam-3759	55	42	by	by	ADP
ejpam-3759	55	43	mt(x	mt(x	NOUN
ejpam-3759	55	44	)	)	PUNCT
ejpam-3759	56	1	=	=	PRON
ejpam-3759	56	2	{	{	PUNCT
ejpam-3759	56	3	t	t	NOUN
ejpam-3759	56	4	x	x	PUNCT
ejpam-3759	56	5	=	=	PUNCT
ejpam-3759	56	6	m	m	PROPN
ejpam-3759	56	7	,	,	PUNCT
ejpam-3759	56	8	0	0	NUM
ejpam-3759	56	9	x	x	SYM
ejpam-3759	56	10	6=	6=	ADP
ejpam-3759	56	11	m	m	VERB
ejpam-3759	56	12	(	(	PUNCT
ejpam-3759	56	13	see	see	VERB
ejpam-3759	56	14	[	[	X
ejpam-3759	56	15	15	15	NUM
ejpam-3759	56	16	]	]	NUM
ejpam-3759	56	17	)	)	PUNCT
ejpam-3759	56	18	.	.	PUNCT
ejpam-3759	57	1	2	2	X
ejpam-3759	57	2	.	.	X
ejpam-3759	57	3	almost	almost	ADV
ejpam-3759	57	4	bi	bi	ADJ
ejpam-3759	57	5	-	-	ADJ
ejpam-3759	57	6	γ	γ	NOUN
ejpam-3759	57	7	-	-	PUNCT
ejpam-3759	57	8	ideals	ideal	NOUN
ejpam-3759	57	9	first	first	ADV
ejpam-3759	57	10	,	,	PUNCT
ejpam-3759	57	11	we	we	PRON
ejpam-3759	57	12	define	define	VERB
ejpam-3759	57	13	almost	almost	ADV
ejpam-3759	57	14	bi	bi	ADJ
ejpam-3759	57	15	-	-	ADJ
ejpam-3759	57	16	γ	γ	NOUN
ejpam-3759	57	17	-	-	PUNCT
ejpam-3759	57	18	ideals	ideal	NOUN
ejpam-3759	57	19	of	of	ADP
ejpam-3759	57	20	γ	γ	NOUN
ejpam-3759	57	21	-	-	PUNCT
ejpam-3759	57	22	semigroups	semigroup	NOUN
ejpam-3759	57	23	as	as	SCONJ
ejpam-3759	57	24	follows	follow	VERB
ejpam-3759	57	25	:	:	PUNCT
ejpam-3759	57	26	definition	definition	NOUN
ejpam-3759	57	27	3	3	NUM
ejpam-3759	57	28	.	.	PUNCT
ejpam-3759	57	29	a	a	DET
ejpam-3759	57	30	non	non	ADJ
ejpam-3759	57	31	-	-	ADJ
ejpam-3759	57	32	empty	empty	ADJ
ejpam-3759	57	33	subset	subset	NOUN
ejpam-3759	57	34	b	b	NOUN
ejpam-3759	57	35	of	of	ADP
ejpam-3759	57	36	a	a	DET
ejpam-3759	57	37	γ	γ	PROPN
ejpam-3759	57	38	-	-	PUNCT
ejpam-3759	57	39	semigroup	semigroup	NOUN
ejpam-3759	57	40	m	m	VERB
ejpam-3759	57	41	is	be	AUX
ejpam-3759	57	42	called	call	VERB
ejpam-3759	57	43	an	an	DET
ejpam-3759	57	44	almost	almost	ADV
ejpam-3759	57	45	bi	bi	ADJ
ejpam-3759	57	46	-	-	ADJ
ejpam-3759	57	47	γ	γ	NOUN
ejpam-3759	57	48	-	-	NOUN
ejpam-3759	57	49	ideal	ideal	NOUN
ejpam-3759	57	50	of	of	ADP
ejpam-3759	57	51	s	s	PRON
ejpam-3759	57	52	if	if	SCONJ
ejpam-3759	57	53	bγmγb	bγmγb	VERB
ejpam-3759	57	54	∩b	∩b	PROPN
ejpam-3759	57	55	6=	6=	NOUN
ejpam-3759	57	56	∅	∅	NOUN
ejpam-3759	57	57	for	for	ADP
ejpam-3759	57	58	all	all	DET
ejpam-3759	57	59	m	m	NOUN
ejpam-3759	57	60	∈m	∈m	NOUN
ejpam-3759	57	61	.	.	PUNCT
ejpam-3759	58	1	example	example	NOUN
ejpam-3759	59	1	1	1	NUM
ejpam-3759	59	2	.	.	PUNCT
ejpam-3759	60	1	let	let	VERB
ejpam-3759	60	2	b	b	X
ejpam-3759	60	3	be	be	AUX
ejpam-3759	60	4	any	any	DET
ejpam-3759	60	5	bi	bi	ADJ
ejpam-3759	60	6	-	-	ADJ
ejpam-3759	60	7	γ	γ	NOUN
ejpam-3759	60	8	-	-	NOUN
ejpam-3759	60	9	ideal	ideal	NOUN
ejpam-3759	60	10	of	of	ADP
ejpam-3759	60	11	a	a	DET
ejpam-3759	60	12	γ	γ	NOUN
ejpam-3759	60	13	-	-	PUNCT
ejpam-3759	60	14	semigroup	semigroup	ADJ
ejpam-3759	60	15	m	m	NOUN
ejpam-3759	60	16	.	.	PUNCT
ejpam-3759	61	1	then	then	ADV
ejpam-3759	61	2	bγmγb	bγmγb	VERB
ejpam-3759	61	3	⊆	⊆	NUM
ejpam-3759	61	4	b.	b.	NOUN
ejpam-3759	61	5	this	this	PRON
ejpam-3759	61	6	implies	imply	VERB
ejpam-3759	61	7	that	that	SCONJ
ejpam-3759	61	8	for	for	ADP
ejpam-3759	61	9	any	any	DET
ejpam-3759	61	10	m	m	NOUN
ejpam-3759	61	11	∈	∈	PROPN
ejpam-3759	61	12	m	m	NOUN
ejpam-3759	61	13	,	,	PUNCT
ejpam-3759	61	14	bγmγb	bγmγb	VERB
ejpam-3759	61	15	⊆	⊆	NUM
ejpam-3759	61	16	bγmγb	bγmγb	X
ejpam-3759	61	17	⊆	⊆	NUM
ejpam-3759	61	18	b.	b.	NOUN
ejpam-3759	61	19	so	so	ADV
ejpam-3759	61	20	bγmγb	bγmγb	X
ejpam-3759	61	21	∩	∩	ADJ
ejpam-3759	61	22	b	b	NOUN
ejpam-3759	61	23	=	=	SYM
ejpam-3759	61	24	bγmγb	bγmγb	X
ejpam-3759	61	25	6=	6=	NUM
ejpam-3759	61	26	∅	∅	NOUN
ejpam-3759	61	27	for	for	ADP
ejpam-3759	61	28	all	all	DET
ejpam-3759	61	29	m	m	NOUN
ejpam-3759	61	30	∈m	∈m	NOUN
ejpam-3759	61	31	.	.	PUNCT
ejpam-3759	62	1	then	then	ADV
ejpam-3759	62	2	b	b	X
ejpam-3759	62	3	is	be	AUX
ejpam-3759	62	4	an	an	DET
ejpam-3759	62	5	almost	almost	ADV
ejpam-3759	62	6	bi	bi	ADJ
ejpam-3759	62	7	-	-	ADJ
ejpam-3759	62	8	γ	γ	NOUN
ejpam-3759	62	9	-	-	NOUN
ejpam-3759	62	10	ideal	ideal	NOUN
ejpam-3759	62	11	of	of	ADP
ejpam-3759	62	12	m	m	PRON
ejpam-3759	62	13	.	.	PUNCT
ejpam-3759	63	1	by	by	ADP
ejpam-3759	63	2	example	example	NOUN
ejpam-3759	63	3	1	1	NUM
ejpam-3759	63	4	,	,	PUNCT
ejpam-3759	63	5	we	we	PRON
ejpam-3759	63	6	conclude	conclude	VERB
ejpam-3759	63	7	that	that	SCONJ
ejpam-3759	63	8	every	every	DET
ejpam-3759	63	9	bi	bi	ADJ
ejpam-3759	63	10	-	-	ADJ
ejpam-3759	63	11	γ	γ	NOUN
ejpam-3759	63	12	-	-	NOUN
ejpam-3759	63	13	ideal	ideal	NOUN
ejpam-3759	63	14	of	of	ADP
ejpam-3759	63	15	a	a	DET
ejpam-3759	63	16	γ	γ	NOUN
ejpam-3759	63	17	-	-	PUNCT
ejpam-3759	63	18	semigroup	semigroup	NOUN
ejpam-3759	63	19	m	m	VERB
ejpam-3759	63	20	is	be	AUX
ejpam-3759	63	21	an	an	DET
ejpam-3759	63	22	almost	almost	ADV
ejpam-3759	63	23	bi	bi	ADJ
ejpam-3759	63	24	-	-	ADJ
ejpam-3759	63	25	γ	γ	NOUN
ejpam-3759	63	26	-	-	NOUN
ejpam-3759	63	27	ideal	ideal	NOUN
ejpam-3759	63	28	of	of	ADP
ejpam-3759	63	29	m	m	PROPN
ejpam-3759	63	30	.	.	PUNCT
ejpam-3759	64	1	example	example	NOUN
ejpam-3759	65	1	2	2	NUM
ejpam-3759	65	2	.	.	X
ejpam-3759	65	3	consider	consider	VERB
ejpam-3759	65	4	the	the	DET
ejpam-3759	65	5	γ	γ	NOUN
ejpam-3759	65	6	-	-	PUNCT
ejpam-3759	65	7	semigroup	semigroup	PROPN
ejpam-3759	65	8	z8	z8	NOUN
ejpam-3759	65	9	with	with	ADP
ejpam-3759	65	10	γ	γ	X
ejpam-3759	65	11	=	=	SYM
ejpam-3759	65	12	{	{	PUNCT
ejpam-3759	65	13	0	0	NUM
ejpam-3759	65	14	,	,	PUNCT
ejpam-3759	65	15	1	1	NUM
ejpam-3759	65	16	,	,	PUNCT
ejpam-3759	65	17	2	2	NUM
ejpam-3759	65	18	}	}	PUNCT
ejpam-3759	65	19	under	under	ADP
ejpam-3759	65	20	the	the	DET
ejpam-3759	65	21	usual	usual	ADJ
ejpam-3759	65	22	addition	addition	NOUN
ejpam-3759	65	23	.	.	PUNCT
ejpam-3759	66	1	let	let	VERB
ejpam-3759	66	2	b	b	NOUN
ejpam-3759	66	3	=	=	PUNCT
ejpam-3759	66	4	{	{	PUNCT
ejpam-3759	66	5	4	4	NUM
ejpam-3759	66	6	,	,	PUNCT
ejpam-3759	66	7	6	6	NUM
ejpam-3759	66	8	}	}	PUNCT
ejpam-3759	66	9	.	.	PUNCT
ejpam-3759	67	1	we	we	PRON
ejpam-3759	67	2	see	see	VERB
ejpam-3759	67	3	that	that	SCONJ
ejpam-3759	67	4	r.	r.	PROPN
ejpam-3759	67	5	chinram	chinram	PROPN
ejpam-3759	67	6	et	et	PROPN
ejpam-3759	67	7	al	al	PROPN
ejpam-3759	67	8	.	.	PUNCT
ejpam-3759	67	9	/	/	SYM
ejpam-3759	67	10	eur	eur	PROPN
ejpam-3759	67	11	.	.	PUNCT
ejpam-3759	68	1	j.	j.	PROPN
ejpam-3759	68	2	pure	pure	PROPN
ejpam-3759	68	3	appl	appl	PROPN
ejpam-3759	68	4	.	.	PROPN
ejpam-3759	68	5	math	math	PROPN
ejpam-3759	68	6	,	,	PUNCT
ejpam-3759	68	7	13	13	NUM
ejpam-3759	68	8	(	(	PUNCT
ejpam-3759	68	9	3	3	NUM
ejpam-3759	68	10	)	)	PUNCT
ejpam-3759	68	11	(	(	PUNCT
ejpam-3759	68	12	2020	2020	NUM
ejpam-3759	68	13	)	)	PUNCT
ejpam-3759	68	14	,	,	PUNCT
ejpam-3759	68	15	620	620	NUM
ejpam-3759	68	16	-	-	SYM
ejpam-3759	68	17	630	630	NUM
ejpam-3759	68	18	623	623	NUM
ejpam-3759	68	19	(	(	PUNCT
ejpam-3759	68	20	b	b	NOUN
ejpam-3759	68	21	+	+	CCONJ
ejpam-3759	68	22	γ	γ	X
ejpam-3759	68	23	+	+	NOUN
ejpam-3759	68	24	0	0	NUM
ejpam-3759	68	25	+	+	CCONJ
ejpam-3759	68	26	γ	γ	PROPN
ejpam-3759	68	27	+	+	PROPN
ejpam-3759	68	28	b	b	NOUN
ejpam-3759	68	29	)	)	PUNCT
ejpam-3759	68	30	∩b	∩b	NOUN
ejpam-3759	68	31	=	=	SYM
ejpam-3759	68	32	z8	z8	PROPN
ejpam-3759	68	33	∩	∩	NOUN
ejpam-3759	68	34	{	{	PUNCT
ejpam-3759	68	35	4	4	NUM
ejpam-3759	68	36	,	,	PUNCT
ejpam-3759	68	37	6	6	NUM
ejpam-3759	68	38	}	}	SYM
ejpam-3759	68	39	6=	6=	NUM
ejpam-3759	68	40	∅	∅	NOUN
ejpam-3759	68	41	,	,	PUNCT
ejpam-3759	68	42	(	(	PUNCT
ejpam-3759	68	43	b	b	X
ejpam-3759	68	44	+	+	CCONJ
ejpam-3759	68	45	γ	γ	X
ejpam-3759	68	46	+	+	NOUN
ejpam-3759	68	47	1	1	NUM
ejpam-3759	68	48	+	+	CCONJ
ejpam-3759	68	49	γ	γ	PROPN
ejpam-3759	68	50	+	+	PROPN
ejpam-3759	68	51	b	b	NOUN
ejpam-3759	68	52	)	)	PUNCT
ejpam-3759	68	53	∩b	∩b	NOUN
ejpam-3759	68	54	=	=	SYM
ejpam-3759	68	55	z8	z8	PROPN
ejpam-3759	68	56	∩	∩	NOUN
ejpam-3759	68	57	{	{	PUNCT
ejpam-3759	68	58	4	4	NUM
ejpam-3759	68	59	,	,	PUNCT
ejpam-3759	68	60	6	6	NUM
ejpam-3759	68	61	}	}	SYM
ejpam-3759	68	62	6=	6=	NUM
ejpam-3759	68	63	∅	∅	NOUN
ejpam-3759	68	64	,	,	PUNCT
ejpam-3759	68	65	(	(	PUNCT
ejpam-3759	68	66	b	b	X
ejpam-3759	68	67	+	+	CCONJ
ejpam-3759	68	68	γ	γ	X
ejpam-3759	68	69	+	+	PROPN
ejpam-3759	68	70	2	2	NUM
ejpam-3759	68	71	+	+	CCONJ
ejpam-3759	68	72	γ	γ	PROPN
ejpam-3759	68	73	+	+	PROPN
ejpam-3759	68	74	b	b	NOUN
ejpam-3759	68	75	)	)	PUNCT
ejpam-3759	68	76	∩b	∩b	NOUN
ejpam-3759	68	77	=	=	SYM
ejpam-3759	68	78	z8	z8	PROPN
ejpam-3759	68	79	∩	∩	NOUN
ejpam-3759	68	80	{	{	PUNCT
ejpam-3759	68	81	4	4	NUM
ejpam-3759	68	82	,	,	PUNCT
ejpam-3759	68	83	6	6	NUM
ejpam-3759	68	84	}	}	SYM
ejpam-3759	68	85	6=	6=	NUM
ejpam-3759	68	86	∅	∅	NOUN
ejpam-3759	68	87	,	,	PUNCT
ejpam-3759	68	88	(	(	PUNCT
ejpam-3759	68	89	b	b	X
ejpam-3759	68	90	+	+	CCONJ
ejpam-3759	68	91	γ	γ	X
ejpam-3759	68	92	+	+	CCONJ
ejpam-3759	68	93	3	3	NUM
ejpam-3759	68	94	+	+	CCONJ
ejpam-3759	68	95	γ	γ	PROPN
ejpam-3759	68	96	+	+	PROPN
ejpam-3759	68	97	b	b	NOUN
ejpam-3759	68	98	)	)	PUNCT
ejpam-3759	68	99	∩b	∩b	NOUN
ejpam-3759	68	100	=	=	SYM
ejpam-3759	68	101	z8	z8	PROPN
ejpam-3759	68	102	∩	∩	NOUN
ejpam-3759	68	103	{	{	PUNCT
ejpam-3759	68	104	4	4	NUM
ejpam-3759	68	105	,	,	PUNCT
ejpam-3759	68	106	6	6	NUM
ejpam-3759	68	107	}	}	SYM
ejpam-3759	68	108	6=	6=	NUM
ejpam-3759	68	109	∅	∅	NOUN
ejpam-3759	68	110	,	,	PUNCT
ejpam-3759	68	111	(	(	PUNCT
ejpam-3759	68	112	b	b	X
ejpam-3759	68	113	+	+	CCONJ
ejpam-3759	68	114	γ	γ	X
ejpam-3759	68	115	+	+	CCONJ
ejpam-3759	68	116	4	4	NUM
ejpam-3759	68	117	+	+	CCONJ
ejpam-3759	68	118	γ	γ	PROPN
ejpam-3759	68	119	+	+	PROPN
ejpam-3759	68	120	b	b	NOUN
ejpam-3759	68	121	)	)	PUNCT
ejpam-3759	68	122	∩b	∩b	NOUN
ejpam-3759	68	123	=	=	SYM
ejpam-3759	68	124	z8	z8	PROPN
ejpam-3759	68	125	∩	∩	NOUN
ejpam-3759	68	126	{	{	PUNCT
ejpam-3759	68	127	4	4	NUM
ejpam-3759	68	128	,	,	PUNCT
ejpam-3759	68	129	6	6	NUM
ejpam-3759	68	130	}	}	SYM
ejpam-3759	68	131	6=	6=	NUM
ejpam-3759	68	132	∅	∅	NOUN
ejpam-3759	68	133	,	,	PUNCT
ejpam-3759	68	134	(	(	PUNCT
ejpam-3759	68	135	b	b	X
ejpam-3759	68	136	+	+	CCONJ
ejpam-3759	68	137	γ	γ	X
ejpam-3759	68	138	+	+	X
ejpam-3759	68	139	5	5	NUM
ejpam-3759	68	140	+	+	CCONJ
ejpam-3759	68	141	γ	γ	PROPN
ejpam-3759	68	142	+	+	PROPN
ejpam-3759	68	143	b	b	NOUN
ejpam-3759	68	144	)	)	PUNCT
ejpam-3759	68	145	∩b	∩b	NOUN
ejpam-3759	68	146	=	=	SYM
ejpam-3759	68	147	z8	z8	PROPN
ejpam-3759	68	148	∩	∩	NOUN
ejpam-3759	68	149	{	{	PUNCT
ejpam-3759	68	150	4	4	NUM
ejpam-3759	68	151	,	,	PUNCT
ejpam-3759	68	152	6	6	NUM
ejpam-3759	68	153	}	}	SYM
ejpam-3759	68	154	6=	6=	NUM
ejpam-3759	68	155	∅	∅	NOUN
ejpam-3759	68	156	,	,	PUNCT
ejpam-3759	68	157	(	(	PUNCT
ejpam-3759	68	158	b	b	X
ejpam-3759	68	159	+	+	CCONJ
ejpam-3759	68	160	γ	γ	X
ejpam-3759	68	161	+	+	PROPN
ejpam-3759	68	162	6	6	NUM
ejpam-3759	68	163	+	+	CCONJ
ejpam-3759	68	164	γ	γ	PROPN
ejpam-3759	68	165	+	+	PROPN
ejpam-3759	68	166	b	b	NOUN
ejpam-3759	68	167	)	)	PUNCT
ejpam-3759	68	168	∩b	∩b	NOUN
ejpam-3759	68	169	=	=	SYM
ejpam-3759	68	170	z8	z8	PROPN
ejpam-3759	68	171	∩	∩	NOUN
ejpam-3759	68	172	{	{	PUNCT
ejpam-3759	68	173	4	4	NUM
ejpam-3759	68	174	,	,	PUNCT
ejpam-3759	68	175	6	6	NUM
ejpam-3759	68	176	}	}	SYM
ejpam-3759	68	177	6=	6=	NUM
ejpam-3759	68	178	∅	∅	NOUN
ejpam-3759	68	179	,	,	PUNCT
ejpam-3759	68	180	(	(	PUNCT
ejpam-3759	68	181	b	b	X
ejpam-3759	68	182	+	+	CCONJ
ejpam-3759	68	183	γ	γ	X
ejpam-3759	68	184	+	+	CCONJ
ejpam-3759	68	185	7	7	NUM
ejpam-3759	68	186	+	+	CCONJ
ejpam-3759	68	187	γ	γ	PROPN
ejpam-3759	68	188	+	+	PROPN
ejpam-3759	68	189	b	b	NOUN
ejpam-3759	68	190	)	)	PUNCT
ejpam-3759	68	191	∩b	∩b	NOUN
ejpam-3759	68	192	=	=	SYM
ejpam-3759	68	193	z8	z8	PROPN
ejpam-3759	68	194	∩	∩	NOUN
ejpam-3759	68	195	{	{	PUNCT
ejpam-3759	68	196	4	4	NUM
ejpam-3759	68	197	,	,	PUNCT
ejpam-3759	68	198	6	6	NUM
ejpam-3759	68	199	}	}	PUNCT
ejpam-3759	68	200	6=	6=	ADP
ejpam-3759	68	201	∅.	∅.	ADP
ejpam-3759	68	202	therefore	therefore	ADV
ejpam-3759	68	203	,	,	PUNCT
ejpam-3759	68	204	b	b	PROPN
ejpam-3759	68	205	is	be	AUX
ejpam-3759	68	206	an	an	DET
ejpam-3759	68	207	almost	almost	ADV
ejpam-3759	68	208	bi	bi	ADJ
ejpam-3759	68	209	-	-	ADJ
ejpam-3759	68	210	γ	γ	NOUN
ejpam-3759	68	211	-	-	NOUN
ejpam-3759	68	212	ideal	ideal	NOUN
ejpam-3759	68	213	of	of	ADP
ejpam-3759	68	214	z8	z8	PROPN
ejpam-3759	68	215	.	.	PUNCT
ejpam-3759	69	1	however	however	ADV
ejpam-3759	69	2	,	,	PUNCT
ejpam-3759	69	3	b	b	PROPN
ejpam-3759	69	4	is	be	AUX
ejpam-3759	69	5	not	not	PART
ejpam-3759	69	6	a	a	DET
ejpam-3759	69	7	bi	bi	ADJ
ejpam-3759	69	8	-	-	ADJ
ejpam-3759	69	9	γ	γ	NOUN
ejpam-3759	69	10	-	-	NOUN
ejpam-3759	69	11	ideal	ideal	NOUN
ejpam-3759	69	12	of	of	ADP
ejpam-3759	69	13	z8	z8	NOUN
ejpam-3759	69	14	because	because	SCONJ
ejpam-3759	69	15	b	b	PROPN
ejpam-3759	69	16	+	+	CCONJ
ejpam-3759	69	17	γ	γ	PROPN
ejpam-3759	69	18	+	+	ADJ
ejpam-3759	69	19	z8	z8	NOUN
ejpam-3759	69	20	+	+	CCONJ
ejpam-3759	69	21	γ	γ	PROPN
ejpam-3759	69	22	+	+	PROPN
ejpam-3759	69	23	b	b	NOUN
ejpam-3759	69	24	=	=	SYM
ejpam-3759	69	25	z8	z8	PROPN
ejpam-3759	69	26	6⊆	6⊆	PROPN
ejpam-3759	69	27	b.	b.	PROPN
ejpam-3759	69	28	from	from	ADP
ejpam-3759	69	29	example	example	NOUN
ejpam-3759	69	30	2	2	NUM
ejpam-3759	69	31	,	,	PUNCT
ejpam-3759	69	32	we	we	PRON
ejpam-3759	69	33	see	see	VERB
ejpam-3759	69	34	that	that	SCONJ
ejpam-3759	69	35	an	an	DET
ejpam-3759	69	36	almost	almost	ADV
ejpam-3759	69	37	bi	bi	ADJ
ejpam-3759	69	38	-	-	ADJ
ejpam-3759	69	39	γ	γ	NOUN
ejpam-3759	69	40	-	-	NOUN
ejpam-3759	69	41	ideal	ideal	NOUN
ejpam-3759	69	42	of	of	ADP
ejpam-3759	69	43	γ	γ	PROPN
ejpam-3759	69	44	-	-	PUNCT
ejpam-3759	69	45	semigroup	semigroup	NOUN
ejpam-3759	69	46	s	s	PART
ejpam-3759	69	47	need	need	AUX
ejpam-3759	69	48	not	not	PART
ejpam-3759	69	49	be	be	AUX
ejpam-3759	69	50	a	a	DET
ejpam-3759	69	51	bi	bi	ADJ
ejpam-3759	69	52	-	-	ADJ
ejpam-3759	69	53	γ	γ	NOUN
ejpam-3759	69	54	-	-	NOUN
ejpam-3759	69	55	ideal	ideal	NOUN
ejpam-3759	69	56	of	of	ADP
ejpam-3759	69	57	s.	s.	PROPN
ejpam-3759	69	58	example	example	PROPN
ejpam-3759	70	1	3	3	X
ejpam-3759	70	2	.	.	PUNCT
ejpam-3759	70	3	consider	consider	VERB
ejpam-3759	70	4	the	the	DET
ejpam-3759	70	5	γ	γ	NOUN
ejpam-3759	70	6	-	-	PUNCT
ejpam-3759	70	7	semigroup	semigroup	NOUN
ejpam-3759	70	8	m	m	NOUN
ejpam-3759	70	9	=	=	PUNCT
ejpam-3759	70	10	{	{	PUNCT
ejpam-3759	70	11	a	a	PRON
ejpam-3759	70	12	,	,	PUNCT
ejpam-3759	70	13	b	b	NOUN
ejpam-3759	70	14	,	,	PUNCT
ejpam-3759	70	15	c	c	NOUN
ejpam-3759	70	16	,	,	PUNCT
ejpam-3759	70	17	d	d	NOUN
ejpam-3759	70	18	}	}	PUNCT
ejpam-3759	70	19	with	with	ADP
ejpam-3759	70	20	γ	γ	X
ejpam-3759	70	21	=	=	SYM
ejpam-3759	70	22	{	{	PUNCT
ejpam-3759	70	23	α	α	NOUN
ejpam-3759	70	24	,	,	PUNCT
ejpam-3759	70	25	β	β	NOUN
ejpam-3759	70	26	}	}	PUNCT
ejpam-3759	70	27	and	and	CCONJ
ejpam-3759	70	28	the	the	DET
ejpam-3759	70	29	multiplication	multiplication	NOUN
ejpam-3759	70	30	table	table	NOUN
ejpam-3759	70	31	:	:	PUNCT
ejpam-3759	70	32	α	α	X
ejpam-3759	71	1	a	a	DET
ejpam-3759	71	2	b	b	NOUN
ejpam-3759	71	3	c	c	NOUN
ejpam-3759	71	4	d	d	NOUN
ejpam-3759	71	5	a	a	PRON
ejpam-3759	71	6	a	a	PRON
ejpam-3759	71	7	c	c	NOUN
ejpam-3759	71	8	c	c	NOUN
ejpam-3759	71	9	a	a	DET
ejpam-3759	71	10	b	b	X
ejpam-3759	71	11	c	c	NOUN
ejpam-3759	71	12	a	a	PRON
ejpam-3759	71	13	a	a	NOUN
ejpam-3759	71	14	c	c	NOUN
ejpam-3759	71	15	c	c	NOUN
ejpam-3759	71	16	c	c	NOUN
ejpam-3759	71	17	a	a	DET
ejpam-3759	71	18	a	a	PRON
ejpam-3759	71	19	c	c	NOUN
ejpam-3759	71	20	d	d	NOUN
ejpam-3759	71	21	a	a	DET
ejpam-3759	71	22	c	c	NOUN
ejpam-3759	71	23	c	c	PROPN
ejpam-3759	71	24	a	a	DET
ejpam-3759	71	25	β	β	X
ejpam-3759	71	26	a	a	DET
ejpam-3759	71	27	b	b	NOUN
ejpam-3759	71	28	c	c	NOUN
ejpam-3759	71	29	d	d	NOUN
ejpam-3759	71	30	a	a	PROPN
ejpam-3759	71	31	c	c	NOUN
ejpam-3759	71	32	a	a	DET
ejpam-3759	71	33	a	a	DET
ejpam-3759	71	34	c	c	NOUN
ejpam-3759	71	35	b	b	PROPN
ejpam-3759	71	36	a	a	DET
ejpam-3759	71	37	c	c	NOUN
ejpam-3759	71	38	c	c	NOUN
ejpam-3759	71	39	a	a	DET
ejpam-3759	71	40	c	c	NOUN
ejpam-3759	71	41	a	a	DET
ejpam-3759	71	42	c	c	NOUN
ejpam-3759	71	43	c	c	NOUN
ejpam-3759	71	44	a	a	PRON
ejpam-3759	71	45	d	d	X
ejpam-3759	71	46	c	c	PROPN
ejpam-3759	71	47	a	a	DET
ejpam-3759	71	48	a	a	DET
ejpam-3759	71	49	c	c	NOUN
ejpam-3759	71	50	let	let	NOUN
ejpam-3759	71	51	b	b	X
ejpam-3759	71	52	=	=	PRON
ejpam-3759	71	53	{	{	PUNCT
ejpam-3759	71	54	a	a	X
ejpam-3759	71	55	,	,	PUNCT
ejpam-3759	71	56	c	c	NOUN
ejpam-3759	71	57	}	}	PUNCT
ejpam-3759	71	58	.	.	PUNCT
ejpam-3759	72	1	then	then	ADV
ejpam-3759	72	2	bγaγb	bγaγb	VERB
ejpam-3759	72	3	∩b	∩b	NOUN
ejpam-3759	72	4	=	=	PRON
ejpam-3759	72	5	{	{	PUNCT
ejpam-3759	72	6	a	a	X
ejpam-3759	72	7	,	,	PUNCT
ejpam-3759	72	8	c	c	NOUN
ejpam-3759	72	9	}	}	PUNCT
ejpam-3759	72	10	∩	∩	NOUN
ejpam-3759	72	11	{	{	PUNCT
ejpam-3759	72	12	a	a	PRON
ejpam-3759	72	13	,	,	PUNCT
ejpam-3759	72	14	c	c	NOUN
ejpam-3759	72	15	}	}	PUNCT
ejpam-3759	72	16	=	=	SYM
ejpam-3759	72	17	{	{	PUNCT
ejpam-3759	72	18	a	a	X
ejpam-3759	72	19	,	,	PUNCT
ejpam-3759	72	20	c	c	NOUN
ejpam-3759	72	21	}	}	PUNCT
ejpam-3759	72	22	6=	6=	NOUN
ejpam-3759	72	23	∅	∅	NOUN
ejpam-3759	72	24	,	,	PUNCT
ejpam-3759	72	25	bγbγb	bγbγb	NOUN
ejpam-3759	72	26	∩b	∩b	NOUN
ejpam-3759	72	27	=	=	PUNCT
ejpam-3759	72	28	{	{	PUNCT
ejpam-3759	72	29	a	a	X
ejpam-3759	72	30	,	,	PUNCT
ejpam-3759	72	31	c	c	NOUN
ejpam-3759	72	32	}	}	PUNCT
ejpam-3759	72	33	∩	∩	NOUN
ejpam-3759	72	34	{	{	PUNCT
ejpam-3759	72	35	a	a	PRON
ejpam-3759	72	36	,	,	PUNCT
ejpam-3759	72	37	c	c	NOUN
ejpam-3759	72	38	}	}	PUNCT
ejpam-3759	72	39	=	=	SYM
ejpam-3759	72	40	{	{	PUNCT
ejpam-3759	72	41	a	a	X
ejpam-3759	72	42	,	,	PUNCT
ejpam-3759	72	43	c	c	NOUN
ejpam-3759	72	44	}	}	PUNCT
ejpam-3759	72	45	6=	6=	NOUN
ejpam-3759	72	46	∅	∅	NOUN
ejpam-3759	72	47	,	,	PUNCT
ejpam-3759	72	48	bγcγb	bγcγb	ADJ
ejpam-3759	72	49	∩b	∩b	NOUN
ejpam-3759	72	50	=	=	PUNCT
ejpam-3759	72	51	{	{	PUNCT
ejpam-3759	72	52	a	a	X
ejpam-3759	72	53	,	,	PUNCT
ejpam-3759	72	54	c	c	NOUN
ejpam-3759	72	55	}	}	PUNCT
ejpam-3759	72	56	∩	∩	NOUN
ejpam-3759	72	57	{	{	PUNCT
ejpam-3759	72	58	a	a	PRON
ejpam-3759	72	59	,	,	PUNCT
ejpam-3759	72	60	c	c	NOUN
ejpam-3759	72	61	}	}	PUNCT
ejpam-3759	72	62	=	=	SYM
ejpam-3759	72	63	{	{	PUNCT
ejpam-3759	72	64	a	a	X
ejpam-3759	72	65	,	,	PUNCT
ejpam-3759	72	66	c	c	NOUN
ejpam-3759	72	67	}	}	PUNCT
ejpam-3759	72	68	6=	6=	NOUN
ejpam-3759	72	69	∅	∅	NOUN
ejpam-3759	72	70	,	,	PUNCT
ejpam-3759	72	71	bγdγb	bγdγb	VERB
ejpam-3759	72	72	∩b	∩b	NOUN
ejpam-3759	72	73	=	=	SYM
ejpam-3759	72	74	{	{	PUNCT
ejpam-3759	72	75	a	a	X
ejpam-3759	72	76	,	,	PUNCT
ejpam-3759	72	77	c	c	NOUN
ejpam-3759	72	78	}	}	PUNCT
ejpam-3759	72	79	∩	∩	NOUN
ejpam-3759	72	80	{	{	PUNCT
ejpam-3759	72	81	a	a	PRON
ejpam-3759	72	82	,	,	PUNCT
ejpam-3759	72	83	c	c	NOUN
ejpam-3759	72	84	}	}	PUNCT
ejpam-3759	72	85	=	=	SYM
ejpam-3759	72	86	{	{	PUNCT
ejpam-3759	72	87	a	a	X
ejpam-3759	72	88	,	,	PUNCT
ejpam-3759	72	89	c	c	NOUN
ejpam-3759	72	90	}	}	PUNCT
ejpam-3759	72	91	6=	6=	X
ejpam-3759	72	92	∅.	∅.	ADP
ejpam-3759	72	93	therefore	therefore	ADV
ejpam-3759	72	94	,	,	PUNCT
ejpam-3759	72	95	b	b	PROPN
ejpam-3759	72	96	is	be	AUX
ejpam-3759	72	97	an	an	DET
ejpam-3759	72	98	almost	almost	ADV
ejpam-3759	72	99	bi	bi	ADJ
ejpam-3759	72	100	-	-	ADJ
ejpam-3759	72	101	γ	γ	NOUN
ejpam-3759	72	102	-	-	NOUN
ejpam-3759	72	103	ideal	ideal	NOUN
ejpam-3759	72	104	of	of	ADP
ejpam-3759	72	105	m	m	PROPN
ejpam-3759	72	106	.	.	PUNCT
ejpam-3759	73	1	theorem	theorem	NOUN
ejpam-3759	73	2	1	1	X
ejpam-3759	73	3	.	.	PUNCT
ejpam-3759	73	4	assume	assume	VERB
ejpam-3759	73	5	that	that	SCONJ
ejpam-3759	73	6	b	b	PROPN
ejpam-3759	73	7	is	be	AUX
ejpam-3759	73	8	an	an	DET
ejpam-3759	73	9	almost	almost	ADV
ejpam-3759	73	10	bi	bi	ADJ
ejpam-3759	73	11	-	-	ADJ
ejpam-3759	73	12	γ	γ	NOUN
ejpam-3759	73	13	-	-	NOUN
ejpam-3759	73	14	ideal	ideal	NOUN
ejpam-3759	73	15	of	of	ADP
ejpam-3759	73	16	a	a	DET
ejpam-3759	73	17	γ	γ	NOUN
ejpam-3759	73	18	-	-	PUNCT
ejpam-3759	73	19	semigroup	semigroup	NOUN
ejpam-3759	73	20	m	m	NOUN
ejpam-3759	73	21	.	.	PUNCT
ejpam-3759	74	1	if	if	SCONJ
ejpam-3759	74	2	a	a	PRON
ejpam-3759	74	3	is	be	AUX
ejpam-3759	74	4	any	any	DET
ejpam-3759	74	5	subset	subset	NOUN
ejpam-3759	74	6	of	of	ADP
ejpam-3759	74	7	m	m	AUX
ejpam-3759	74	8	containing	contain	VERB
ejpam-3759	74	9	b	b	NOUN
ejpam-3759	74	10	,	,	PUNCT
ejpam-3759	74	11	then	then	ADV
ejpam-3759	74	12	a	a	PRON
ejpam-3759	74	13	is	be	AUX
ejpam-3759	74	14	also	also	ADV
ejpam-3759	74	15	an	an	DET
ejpam-3759	74	16	almost	almost	ADV
ejpam-3759	74	17	bi	bi	ADJ
ejpam-3759	74	18	-	-	ADJ
ejpam-3759	74	19	γ	γ	NOUN
ejpam-3759	74	20	-	-	NOUN
ejpam-3759	74	21	ideal	ideal	NOUN
ejpam-3759	74	22	of	of	ADP
ejpam-3759	74	23	m	m	PROPN
ejpam-3759	74	24	.	.	PUNCT
ejpam-3759	75	1	proof	proof	NOUN
ejpam-3759	75	2	.	.	PUNCT
ejpam-3759	76	1	since	since	SCONJ
ejpam-3759	76	2	b	b	PROPN
ejpam-3759	76	3	is	be	AUX
ejpam-3759	76	4	an	an	DET
ejpam-3759	76	5	almost	almost	ADV
ejpam-3759	76	6	bi	bi	ADJ
ejpam-3759	76	7	-	-	ADJ
ejpam-3759	76	8	γ	γ	NOUN
ejpam-3759	76	9	-	-	NOUN
ejpam-3759	76	10	ideal	ideal	NOUN
ejpam-3759	76	11	of	of	ADP
ejpam-3759	76	12	m	m	PROPN
ejpam-3759	76	13	and	and	CCONJ
ejpam-3759	76	14	b	b	X
ejpam-3759	76	15	⊆	⊆	NUM
ejpam-3759	76	16	a	a	PRON
ejpam-3759	76	17	,	,	PUNCT
ejpam-3759	76	18	we	we	PRON
ejpam-3759	76	19	have	have	VERB
ejpam-3759	76	20	bγmγb∩b	bγmγb∩b	X
ejpam-3759	76	21	6=	6=	ADP
ejpam-3759	76	22	∅	∅	NOUN
ejpam-3759	76	23	and	and	CCONJ
ejpam-3759	76	24	bγmγb∩b	bγmγb∩b	PROPN
ejpam-3759	77	1	⊆	⊆	NUM
ejpam-3759	77	2	aγmγa∩a	aγmγa∩a	PUNCT
ejpam-3759	77	3	for	for	ADP
ejpam-3759	77	4	all	all	DET
ejpam-3759	77	5	m	m	NOUN
ejpam-3759	77	6	∈m	∈m	NOUN
ejpam-3759	77	7	,	,	PUNCT
ejpam-3759	77	8	respectively	respectively	ADV
ejpam-3759	77	9	.	.	PUNCT
ejpam-3759	78	1	this	this	PRON
ejpam-3759	78	2	implies	imply	VERB
ejpam-3759	78	3	that	that	PRON
ejpam-3759	78	4	aγmγa∩a	aγmγa∩a	PUNCT
ejpam-3759	78	5	6=	6=	ADP
ejpam-3759	78	6	∅	∅	NOUN
ejpam-3759	78	7	for	for	ADP
ejpam-3759	78	8	all	all	DET
ejpam-3759	78	9	m	m	NOUN
ejpam-3759	78	10	∈m	∈m	NOUN
ejpam-3759	78	11	.	.	PUNCT
ejpam-3759	79	1	therefore	therefore	ADV
ejpam-3759	79	2	,	,	PUNCT
ejpam-3759	79	3	a	a	PRON
ejpam-3759	79	4	is	be	AUX
ejpam-3759	79	5	an	an	DET
ejpam-3759	79	6	almost	almost	ADV
ejpam-3759	79	7	bi	bi	ADJ
ejpam-3759	79	8	-	-	ADJ
ejpam-3759	79	9	γ	γ	NOUN
ejpam-3759	79	10	-	-	NOUN
ejpam-3759	79	11	ideal	ideal	NOUN
ejpam-3759	79	12	of	of	ADP
ejpam-3759	79	13	m	m	PROPN
ejpam-3759	79	14	.	.	PUNCT
ejpam-3759	80	1	corollary	corollary	ADJ
ejpam-3759	80	2	1	1	NUM
ejpam-3759	80	3	.	.	PUNCT
ejpam-3759	81	1	the	the	DET
ejpam-3759	81	2	union	union	NOUN
ejpam-3759	81	3	of	of	ADP
ejpam-3759	81	4	any	any	DET
ejpam-3759	81	5	two	two	NUM
ejpam-3759	81	6	almost	almost	ADV
ejpam-3759	81	7	bi	bi	ADJ
ejpam-3759	81	8	-	-	ADJ
ejpam-3759	81	9	γ	γ	NOUN
ejpam-3759	81	10	-	-	PUNCT
ejpam-3759	81	11	ideals	ideal	NOUN
ejpam-3759	81	12	of	of	ADP
ejpam-3759	81	13	a	a	DET
ejpam-3759	81	14	γ	γ	PROPN
ejpam-3759	81	15	-	-	PUNCT
ejpam-3759	81	16	semigroup	semigroup	NOUN
ejpam-3759	81	17	m	m	VERB
ejpam-3759	81	18	is	be	AUX
ejpam-3759	81	19	also	also	ADV
ejpam-3759	81	20	an	an	DET
ejpam-3759	81	21	almost	almost	ADV
ejpam-3759	81	22	bi	bi	ADJ
ejpam-3759	81	23	-	-	ADJ
ejpam-3759	81	24	γ	γ	NOUN
ejpam-3759	81	25	-	-	NOUN
ejpam-3759	81	26	ideal	ideal	NOUN
ejpam-3759	81	27	of	of	ADP
ejpam-3759	81	28	m	m	PROPN
ejpam-3759	81	29	.	.	PUNCT
ejpam-3759	82	1	proof	proof	NOUN
ejpam-3759	82	2	.	.	PUNCT
ejpam-3759	83	1	let	let	VERB
ejpam-3759	83	2	a	a	PRON
ejpam-3759	83	3	and	and	CCONJ
ejpam-3759	83	4	b	b	NOUN
ejpam-3759	83	5	be	be	AUX
ejpam-3759	83	6	any	any	DET
ejpam-3759	83	7	two	two	NUM
ejpam-3759	83	8	almost	almost	ADV
ejpam-3759	83	9	bi	bi	ADJ
ejpam-3759	83	10	-	-	ADJ
ejpam-3759	83	11	γ	γ	NOUN
ejpam-3759	83	12	-	-	PUNCT
ejpam-3759	83	13	ideals	ideal	NOUN
ejpam-3759	83	14	of	of	ADP
ejpam-3759	83	15	m	m	PROPN
ejpam-3759	83	16	.	.	PUNCT
ejpam-3759	84	1	since	since	SCONJ
ejpam-3759	84	2	a	a	DET
ejpam-3759	84	3	⊆	⊆	NUM
ejpam-3759	84	4	a	a	DET
ejpam-3759	84	5	∪	∪	NOUN
ejpam-3759	84	6	b	b	NOUN
ejpam-3759	84	7	⊆	⊆	NUM
ejpam-3759	84	8	m	m	NOUN
ejpam-3759	84	9	,	,	PUNCT
ejpam-3759	84	10	it	it	PRON
ejpam-3759	84	11	follows	follow	VERB
ejpam-3759	84	12	from	from	ADP
ejpam-3759	84	13	theorem	theorem	ADJ
ejpam-3759	84	14	1	1	NUM
ejpam-3759	85	1	that	that	SCONJ
ejpam-3759	85	2	a	a	PRON
ejpam-3759	85	3	∪b	∪b	VERB
ejpam-3759	85	4	is	be	AUX
ejpam-3759	85	5	an	an	DET
ejpam-3759	85	6	almost	almost	ADV
ejpam-3759	85	7	bi	bi	ADJ
ejpam-3759	85	8	-	-	ADJ
ejpam-3759	85	9	γ	γ	NOUN
ejpam-3759	85	10	-	-	NOUN
ejpam-3759	85	11	ideal	ideal	NOUN
ejpam-3759	85	12	of	of	ADP
ejpam-3759	85	13	m	m	PROPN
ejpam-3759	85	14	.	.	PUNCT
ejpam-3759	86	1	r.	r.	PROPN
ejpam-3759	86	2	chinram	chinram	PROPN
ejpam-3759	86	3	et	et	PROPN
ejpam-3759	86	4	al	al	PROPN
ejpam-3759	86	5	.	.	PUNCT
ejpam-3759	86	6	/	/	SYM
ejpam-3759	86	7	eur	eur	PROPN
ejpam-3759	86	8	.	.	PUNCT
ejpam-3759	87	1	j.	j.	PROPN
ejpam-3759	87	2	pure	pure	PROPN
ejpam-3759	87	3	appl	appl	PROPN
ejpam-3759	87	4	.	.	PROPN
ejpam-3759	87	5	math	math	PROPN
ejpam-3759	87	6	,	,	PUNCT
ejpam-3759	87	7	13	13	NUM
ejpam-3759	87	8	(	(	PUNCT
ejpam-3759	87	9	3	3	NUM
ejpam-3759	87	10	)	)	PUNCT
ejpam-3759	87	11	(	(	PUNCT
ejpam-3759	87	12	2020	2020	NUM
ejpam-3759	87	13	)	)	PUNCT
ejpam-3759	87	14	,	,	PUNCT
ejpam-3759	87	15	620	620	NUM
ejpam-3759	87	16	-	-	SYM
ejpam-3759	87	17	630	630	NUM
ejpam-3759	87	18	624	624	NUM
ejpam-3759	87	19	example	example	NOUN
ejpam-3759	87	20	4	4	NUM
ejpam-3759	87	21	.	.	PUNCT
ejpam-3759	87	22	consider	consider	VERB
ejpam-3759	87	23	the	the	DET
ejpam-3759	87	24	γ	γ	NOUN
ejpam-3759	87	25	-	-	PUNCT
ejpam-3759	87	26	semigroup	semigroup	PROPN
ejpam-3759	87	27	z8	z8	NOUN
ejpam-3759	87	28	with	with	ADP
ejpam-3759	87	29	γ	γ	X
ejpam-3759	87	30	=	=	SYM
ejpam-3759	87	31	{	{	PUNCT
ejpam-3759	87	32	0	0	NUM
ejpam-3759	87	33	,	,	PUNCT
ejpam-3759	87	34	1	1	NUM
ejpam-3759	87	35	,	,	PUNCT
ejpam-3759	87	36	2	2	NUM
ejpam-3759	87	37	}	}	PUNCT
ejpam-3759	87	38	under	under	ADP
ejpam-3759	87	39	the	the	DET
ejpam-3759	87	40	usual	usual	ADJ
ejpam-3759	87	41	addition	addition	NOUN
ejpam-3759	87	42	.	.	PUNCT
ejpam-3759	88	1	let	let	VERB
ejpam-3759	88	2	a	a	PRON
ejpam-3759	88	3	=	=	PUNCT
ejpam-3759	88	4	{	{	PUNCT
ejpam-3759	88	5	2	2	NUM
ejpam-3759	88	6	,	,	PUNCT
ejpam-3759	88	7	3	3	NUM
ejpam-3759	88	8	}	}	PUNCT
ejpam-3759	88	9	and	and	CCONJ
ejpam-3759	88	10	b	b	X
ejpam-3759	88	11	=	=	PUNCT
ejpam-3759	88	12	{	{	PUNCT
ejpam-3759	88	13	4	4	NUM
ejpam-3759	88	14	,	,	PUNCT
ejpam-3759	88	15	6	6	NUM
ejpam-3759	88	16	}	}	PUNCT
ejpam-3759	88	17	.	.	PUNCT
ejpam-3759	89	1	clearly	clearly	ADV
ejpam-3759	89	2	,	,	PUNCT
ejpam-3759	89	3	a	a	PRON
ejpam-3759	89	4	and	and	CCONJ
ejpam-3759	89	5	b	b	NOUN
ejpam-3759	89	6	are	be	AUX
ejpam-3759	89	7	almost	almost	ADV
ejpam-3759	89	8	bi	bi	ADJ
ejpam-3759	89	9	-	-	ADJ
ejpam-3759	89	10	γ	γ	NOUN
ejpam-3759	89	11	-	-	PUNCT
ejpam-3759	89	12	ideals	ideal	NOUN
ejpam-3759	89	13	of	of	ADP
ejpam-3759	89	14	z8	z8	NOUN
ejpam-3759	89	15	but	but	CCONJ
ejpam-3759	89	16	a	a	DET
ejpam-3759	89	17	∩b	∩b	NOUN
ejpam-3759	89	18	=	=	SYM
ejpam-3759	89	19	∅	∅	NOUN
ejpam-3759	89	20	,	,	PUNCT
ejpam-3759	89	21	so	so	SCONJ
ejpam-3759	89	22	it	it	PRON
ejpam-3759	89	23	is	be	AUX
ejpam-3759	89	24	not	not	PART
ejpam-3759	89	25	an	an	DET
ejpam-3759	89	26	almost	almost	ADV
ejpam-3759	89	27	bi	bi	ADJ
ejpam-3759	89	28	-	-	ADJ
ejpam-3759	89	29	γ	γ	NOUN
ejpam-3759	89	30	-	-	NOUN
ejpam-3759	89	31	ideal	ideal	NOUN
ejpam-3759	89	32	of	of	ADP
ejpam-3759	89	33	z8	z8	PROPN
ejpam-3759	89	34	.	.	PUNCT
ejpam-3759	90	1	by	by	ADP
ejpam-3759	90	2	example	example	NOUN
ejpam-3759	90	3	4	4	NUM
ejpam-3759	90	4	,	,	PUNCT
ejpam-3759	90	5	we	we	PRON
ejpam-3759	90	6	have	have	VERB
ejpam-3759	90	7	the	the	DET
ejpam-3759	90	8	following	follow	VERB
ejpam-3759	90	9	remark	remark	NOUN
ejpam-3759	90	10	.	.	PUNCT
ejpam-3759	91	1	remark	remark	PROPN
ejpam-3759	91	2	1	1	NUM
ejpam-3759	91	3	.	.	PUNCT
ejpam-3759	92	1	the	the	DET
ejpam-3759	92	2	intersection	intersection	NOUN
ejpam-3759	92	3	of	of	ADP
ejpam-3759	92	4	any	any	DET
ejpam-3759	92	5	two	two	NUM
ejpam-3759	92	6	almost	almost	ADV
ejpam-3759	92	7	bi	bi	ADJ
ejpam-3759	92	8	-	-	ADJ
ejpam-3759	92	9	γ	γ	NOUN
ejpam-3759	92	10	-	-	PUNCT
ejpam-3759	92	11	ideals	ideal	NOUN
ejpam-3759	92	12	of	of	ADP
ejpam-3759	92	13	a	a	DET
ejpam-3759	92	14	γ	γ	PROPN
ejpam-3759	92	15	-	-	PUNCT
ejpam-3759	92	16	semigroup	semigroup	NOUN
ejpam-3759	92	17	m	m	NOUN
ejpam-3759	92	18	need	need	AUX
ejpam-3759	92	19	not	not	PART
ejpam-3759	92	20	be	be	AUX
ejpam-3759	92	21	an	an	DET
ejpam-3759	92	22	almost	almost	ADV
ejpam-3759	92	23	bi	bi	ADJ
ejpam-3759	92	24	-	-	ADJ
ejpam-3759	92	25	γ	γ	NOUN
ejpam-3759	92	26	-	-	NOUN
ejpam-3759	92	27	ideal	ideal	NOUN
ejpam-3759	92	28	of	of	ADP
ejpam-3759	92	29	m	m	PROPN
ejpam-3759	92	30	.	.	PUNCT
ejpam-3759	93	1	theorem	theorem	ADJ
ejpam-3759	93	2	2	2	NUM
ejpam-3759	93	3	.	.	PUNCT
ejpam-3759	93	4	a	a	DET
ejpam-3759	93	5	γ	γ	PROPN
ejpam-3759	93	6	-	-	PUNCT
ejpam-3759	93	7	semigroup	semigroup	NOUN
ejpam-3759	93	8	m	m	VERB
ejpam-3759	93	9	contains	contain	VERB
ejpam-3759	93	10	a	a	DET
ejpam-3759	93	11	proper	proper	ADJ
ejpam-3759	93	12	almost	almost	ADV
ejpam-3759	93	13	bi	bi	ADJ
ejpam-3759	93	14	-	-	ADJ
ejpam-3759	93	15	γ	γ	NOUN
ejpam-3759	93	16	-	-	NOUN
ejpam-3759	93	17	ideal	ideal	NOUN
ejpam-3759	93	18	if	if	SCONJ
ejpam-3759	93	19	and	and	CCONJ
ejpam-3759	93	20	only	only	ADV
ejpam-3759	93	21	if	if	SCONJ
ejpam-3759	93	22	there	there	PRON
ejpam-3759	93	23	exists	exist	VERB
ejpam-3759	93	24	an	an	DET
ejpam-3759	93	25	element	element	NOUN
ejpam-3759	93	26	m	m	NOUN
ejpam-3759	93	27	of	of	ADP
ejpam-3759	93	28	m	m	PRON
ejpam-3759	93	29	such	such	ADJ
ejpam-3759	93	30	that	that	SCONJ
ejpam-3759	93	31	m	m	VERB
ejpam-3759	93	32	r	r	NOUN
ejpam-3759	93	33	{	{	PUNCT
ejpam-3759	93	34	m	m	VERB
ejpam-3759	93	35	}	}	PUNCT
ejpam-3759	93	36	is	be	AUX
ejpam-3759	93	37	an	an	DET
ejpam-3759	93	38	almost	almost	ADV
ejpam-3759	93	39	bi	bi	ADJ
ejpam-3759	93	40	-	-	ADJ
ejpam-3759	93	41	γ	γ	NOUN
ejpam-3759	93	42	-	-	NOUN
ejpam-3759	93	43	ideal	ideal	NOUN
ejpam-3759	93	44	of	of	ADP
ejpam-3759	93	45	m	m	PROPN
ejpam-3759	93	46	.	.	PUNCT
ejpam-3759	94	1	proof	proof	NOUN
ejpam-3759	94	2	.	.	PUNCT
ejpam-3759	95	1	assume	assume	VERB
ejpam-3759	95	2	that	that	SCONJ
ejpam-3759	95	3	a	a	DET
ejpam-3759	95	4	γ	γ	PROPN
ejpam-3759	95	5	-	-	PUNCT
ejpam-3759	95	6	semigroup	semigroup	NOUN
ejpam-3759	95	7	m	m	VERB
ejpam-3759	95	8	contains	contain	VERB
ejpam-3759	95	9	a	a	DET
ejpam-3759	95	10	proper	proper	ADJ
ejpam-3759	95	11	almost	almost	ADV
ejpam-3759	95	12	bi	bi	ADJ
ejpam-3759	95	13	-	-	ADJ
ejpam-3759	95	14	γ	γ	ADJ
ejpam-3759	95	15	-	-	PUNCT
ejpam-3759	95	16	ideal	ideal	NOUN
ejpam-3759	95	17	b	b	NOUN
ejpam-3759	95	18	and	and	CCONJ
ejpam-3759	95	19	let	let	VERB
ejpam-3759	95	20	m	m	PRON
ejpam-3759	95	21	∈m	∈m	ADJ
ejpam-3759	95	22	rb	rb	NOUN
ejpam-3759	95	23	.	.	PUNCT
ejpam-3759	96	1	then	then	ADV
ejpam-3759	96	2	b	b	X
ejpam-3759	96	3	⊆m	⊆m	NOUN
ejpam-3759	96	4	r	r	NOUN
ejpam-3759	96	5	{	{	PUNCT
ejpam-3759	96	6	m	m	NOUN
ejpam-3759	96	7	}	}	PUNCT
ejpam-3759	96	8	⊂m	⊂m	PROPN
ejpam-3759	96	9	.	.	PUNCT
ejpam-3759	97	1	by	by	ADP
ejpam-3759	97	2	theorem	theorem	NOUN
ejpam-3759	97	3	1	1	NUM
ejpam-3759	97	4	,	,	PUNCT
ejpam-3759	97	5	m	m	VERB
ejpam-3759	97	6	r	r	NOUN
ejpam-3759	97	7	{	{	PUNCT
ejpam-3759	97	8	m	m	VERB
ejpam-3759	97	9	}	}	PUNCT
ejpam-3759	97	10	is	be	AUX
ejpam-3759	97	11	an	an	DET
ejpam-3759	97	12	almost	almost	ADV
ejpam-3759	97	13	bi	bi	ADJ
ejpam-3759	97	14	-	-	ADJ
ejpam-3759	97	15	γ	γ	NOUN
ejpam-3759	97	16	-	-	NOUN
ejpam-3759	97	17	ideal	ideal	NOUN
ejpam-3759	97	18	of	of	ADP
ejpam-3759	97	19	m	m	PRON
ejpam-3759	97	20	.	.	PUNCT
ejpam-3759	98	1	conversely	conversely	ADV
ejpam-3759	98	2	,	,	PUNCT
ejpam-3759	98	3	let	let	VERB
ejpam-3759	98	4	m	m	PRON
ejpam-3759	98	5	∈	∈	VERB
ejpam-3759	98	6	m	m	AUX
ejpam-3759	98	7	be	be	VERB
ejpam-3759	98	8	such	such	ADJ
ejpam-3759	98	9	that	that	SCONJ
ejpam-3759	98	10	m	m	VERB
ejpam-3759	98	11	r	r	NOUN
ejpam-3759	98	12	{	{	PUNCT
ejpam-3759	98	13	m	m	VERB
ejpam-3759	98	14	}	}	PUNCT
ejpam-3759	98	15	is	be	AUX
ejpam-3759	98	16	an	an	DET
ejpam-3759	98	17	almost	almost	ADV
ejpam-3759	98	18	bi	bi	ADJ
ejpam-3759	98	19	-	-	ADJ
ejpam-3759	98	20	γ	γ	NOUN
ejpam-3759	98	21	-	-	NOUN
ejpam-3759	98	22	ideal	ideal	NOUN
ejpam-3759	98	23	of	of	ADP
ejpam-3759	98	24	m	m	PROPN
ejpam-3759	98	25	.	.	PUNCT
ejpam-3759	99	1	since	since	SCONJ
ejpam-3759	99	2	m	m	PROPN
ejpam-3759	99	3	r	r	NOUN
ejpam-3759	99	4	{	{	PUNCT
ejpam-3759	99	5	m	m	NOUN
ejpam-3759	99	6	}	}	PUNCT
ejpam-3759	99	7	(	(	PUNCT
ejpam-3759	99	8	m	m	INTJ
ejpam-3759	99	9	,	,	PUNCT
ejpam-3759	99	10	we	we	PRON
ejpam-3759	99	11	get	get	VERB
ejpam-3759	99	12	m	m	VERB
ejpam-3759	99	13	r	r	NOUN
ejpam-3759	99	14	{	{	PUNCT
ejpam-3759	99	15	m	m	VERB
ejpam-3759	99	16	}	}	PUNCT
ejpam-3759	99	17	is	be	AUX
ejpam-3759	99	18	a	a	DET
ejpam-3759	99	19	proper	proper	ADJ
ejpam-3759	99	20	almost	almost	ADV
ejpam-3759	99	21	bi	bi	ADJ
ejpam-3759	99	22	-	-	ADJ
ejpam-3759	99	23	γ	γ	NOUN
ejpam-3759	99	24	-	-	NOUN
ejpam-3759	99	25	ideal	ideal	NOUN
ejpam-3759	99	26	of	of	ADP
ejpam-3759	99	27	m	m	PROPN
ejpam-3759	99	28	.	.	PUNCT
ejpam-3759	100	1	theorem	theorem	ADJ
ejpam-3759	100	2	3	3	X
ejpam-3759	100	3	.	.	PUNCT
ejpam-3759	101	1	let	let	VERB
ejpam-3759	101	2	m	m	PRON
ejpam-3759	101	3	be	be	AUX
ejpam-3759	101	4	a	a	DET
ejpam-3759	101	5	γ	γ	NOUN
ejpam-3759	101	6	-	-	PUNCT
ejpam-3759	101	7	semigroup	semigroup	NOUN
ejpam-3759	102	1	such	such	ADJ
ejpam-3759	102	2	that	that	SCONJ
ejpam-3759	102	3	|m	|m	NOUN
ejpam-3759	102	4	|	|	ADV
ejpam-3759	102	5	>	>	X
ejpam-3759	102	6	1	1	X
ejpam-3759	102	7	.	.	PUNCT
ejpam-3759	102	8	then	then	ADV
ejpam-3759	102	9	m	m	PROPN
ejpam-3759	102	10	has	have	VERB
ejpam-3759	102	11	no	no	DET
ejpam-3759	102	12	proper	proper	ADJ
ejpam-3759	102	13	almost	almost	ADV
ejpam-3759	102	14	bi	bi	ADJ
ejpam-3759	102	15	-	-	ADJ
ejpam-3759	102	16	γ	γ	NOUN
ejpam-3759	102	17	-	-	PUNCT
ejpam-3759	102	18	ideals	ideal	NOUN
ejpam-3759	102	19	if	if	SCONJ
ejpam-3759	102	20	and	and	CCONJ
ejpam-3759	102	21	only	only	ADV
ejpam-3759	102	22	if	if	SCONJ
ejpam-3759	102	23	for	for	ADP
ejpam-3759	102	24	all	all	DET
ejpam-3759	102	25	m	m	NOUN
ejpam-3759	102	26	∈m	∈m	NOUN
ejpam-3759	102	27	there	there	ADV
ejpam-3759	102	28	exists	exist	VERB
ejpam-3759	102	29	a	a	DET
ejpam-3759	102	30	∈m	∈m	NOUN
ejpam-3759	102	31	such	such	ADJ
ejpam-3759	102	32	that	that	SCONJ
ejpam-3759	102	33	(	(	PUNCT
ejpam-3759	102	34	m	m	NOUN
ejpam-3759	102	35	r	r	NOUN
ejpam-3759	102	36	{	{	PUNCT
ejpam-3759	102	37	m})γaγ(m	m})γaγ(m	NOUN
ejpam-3759	102	38	r	r	NOUN
ejpam-3759	102	39	{	{	PUNCT
ejpam-3759	102	40	m	m	NOUN
ejpam-3759	102	41	}	}	PUNCT
ejpam-3759	102	42	)	)	PUNCT
ejpam-3759	102	43	=	=	PUNCT
ejpam-3759	102	44	{	{	PUNCT
ejpam-3759	102	45	m	m	NOUN
ejpam-3759	102	46	}	}	PUNCT
ejpam-3759	102	47	.	.	PUNCT
ejpam-3759	103	1	proof	proof	NOUN
ejpam-3759	103	2	.	.	PUNCT
ejpam-3759	104	1	assume	assume	VERB
ejpam-3759	104	2	that	that	SCONJ
ejpam-3759	104	3	m	m	PROPN
ejpam-3759	104	4	has	have	VERB
ejpam-3759	104	5	no	no	DET
ejpam-3759	104	6	proper	proper	ADJ
ejpam-3759	104	7	almost	almost	ADV
ejpam-3759	104	8	bi	bi	ADJ
ejpam-3759	104	9	-	-	ADJ
ejpam-3759	104	10	γ	γ	NOUN
ejpam-3759	104	11	-	-	PUNCT
ejpam-3759	104	12	ideals	ideal	NOUN
ejpam-3759	104	13	and	and	CCONJ
ejpam-3759	104	14	let	let	VERB
ejpam-3759	104	15	m	m	PRON
ejpam-3759	104	16	∈m	∈m	NOUN
ejpam-3759	104	17	.	.	PUNCT
ejpam-3759	105	1	by	by	ADP
ejpam-3759	105	2	theorem	theorem	NOUN
ejpam-3759	105	3	2	2	NUM
ejpam-3759	105	4	,	,	PUNCT
ejpam-3759	105	5	m	m	VERB
ejpam-3759	105	6	r	r	NOUN
ejpam-3759	105	7	{	{	PUNCT
ejpam-3759	105	8	m	m	VERB
ejpam-3759	105	9	}	}	PUNCT
ejpam-3759	105	10	is	be	AUX
ejpam-3759	105	11	not	not	PART
ejpam-3759	105	12	an	an	DET
ejpam-3759	105	13	almost	almost	ADV
ejpam-3759	105	14	bi	bi	ADJ
ejpam-3759	105	15	-	-	ADJ
ejpam-3759	105	16	γ	γ	NOUN
ejpam-3759	105	17	-	-	NOUN
ejpam-3759	105	18	ideal	ideal	NOUN
ejpam-3759	105	19	of	of	ADP
ejpam-3759	105	20	m	m	PROPN
ejpam-3759	105	21	.	.	PUNCT
ejpam-3759	106	1	thus	thus	ADV
ejpam-3759	106	2	there	there	PRON
ejpam-3759	106	3	exists	exist	VERB
ejpam-3759	106	4	an	an	DET
ejpam-3759	106	5	element	element	NOUN
ejpam-3759	106	6	a	a	PRON
ejpam-3759	106	7	of	of	ADP
ejpam-3759	106	8	m	m	PRON
ejpam-3759	106	9	such	such	ADJ
ejpam-3759	106	10	that	that	SCONJ
ejpam-3759	106	11	(	(	PUNCT
ejpam-3759	106	12	mr{m})γaγ(mr{m})∩(mr{m	mr{m})γaγ(mr{m})∩(mr{m	NOUN
ejpam-3759	106	13	}	}	PUNCT
ejpam-3759	106	14	)	)	PUNCT
ejpam-3759	106	15	=	=	PUNCT
ejpam-3759	106	16	∅.	∅.	VERB
ejpam-3759	106	17	hence	hence	ADV
ejpam-3759	106	18	,	,	PUNCT
ejpam-3759	106	19	(	(	PUNCT
ejpam-3759	106	20	mr{m})γaγ(mr{m	mr{m})γaγ(mr{m	NOUN
ejpam-3759	106	21	}	}	PUNCT
ejpam-3759	106	22	)	)	PUNCT
ejpam-3759	106	23	=	=	PUNCT
ejpam-3759	106	24	{	{	PUNCT
ejpam-3759	106	25	m	m	NOUN
ejpam-3759	106	26	}	}	PUNCT
ejpam-3759	106	27	.	.	PUNCT
ejpam-3759	107	1	conversely	conversely	ADV
ejpam-3759	107	2	,	,	PUNCT
ejpam-3759	107	3	suppose	suppose	VERB
ejpam-3759	107	4	m	m	NOUN
ejpam-3759	107	5	contains	contain	VERB
ejpam-3759	107	6	a	a	DET
ejpam-3759	107	7	proper	proper	ADJ
ejpam-3759	107	8	almost	almost	ADV
ejpam-3759	107	9	bi	bi	ADJ
ejpam-3759	107	10	-	-	ADJ
ejpam-3759	107	11	γ	γ	ADJ
ejpam-3759	107	12	-	-	PUNCT
ejpam-3759	107	13	ideal	ideal	ADJ
ejpam-3759	108	1	b.	b.	PROPN
ejpam-3759	109	1	let	let	VERB
ejpam-3759	109	2	m	m	PRON
ejpam-3759	109	3	∈	∈	VERB
ejpam-3759	109	4	m	m	VERB
ejpam-3759	109	5	r	r	NOUN
ejpam-3759	109	6	b.	b.	NOUN
ejpam-3759	109	7	by	by	ADP
ejpam-3759	109	8	assumption	assumption	NOUN
ejpam-3759	109	9	,	,	PUNCT
ejpam-3759	109	10	we	we	PRON
ejpam-3759	109	11	have	have	VERB
ejpam-3759	109	12	(	(	PUNCT
ejpam-3759	109	13	m	m	VERB
ejpam-3759	109	14	r	r	NOUN
ejpam-3759	109	15	{	{	PUNCT
ejpam-3759	109	16	m})γaγ(m	m})γaγ(m	NOUN
ejpam-3759	109	17	r	r	NOUN
ejpam-3759	109	18	{	{	PUNCT
ejpam-3759	109	19	m	m	NOUN
ejpam-3759	109	20	}	}	PUNCT
ejpam-3759	109	21	)	)	PUNCT
ejpam-3759	110	1	=	=	PRON
ejpam-3759	110	2	{	{	PUNCT
ejpam-3759	110	3	m	m	VERB
ejpam-3759	110	4	}	}	PUNCT
ejpam-3759	110	5	for	for	ADP
ejpam-3759	110	6	some	some	DET
ejpam-3759	110	7	element	element	NOUN
ejpam-3759	110	8	a	a	PRON
ejpam-3759	110	9	in	in	ADP
ejpam-3759	110	10	m	m	PROPN
ejpam-3759	110	11	.	.	PUNCT
ejpam-3759	111	1	since	since	SCONJ
ejpam-3759	111	2	b	b	PROPN
ejpam-3759	111	3	⊆	⊆	NUM
ejpam-3759	111	4	m	m	NOUN
ejpam-3759	111	5	r	r	NOUN
ejpam-3759	111	6	{	{	PUNCT
ejpam-3759	111	7	m	m	NOUN
ejpam-3759	111	8	}	}	PUNCT
ejpam-3759	111	9	⊂	⊂	PROPN
ejpam-3759	111	10	m	m	VERB
ejpam-3759	111	11	,	,	PUNCT
ejpam-3759	111	12	we	we	PRON
ejpam-3759	111	13	get	get	VERB
ejpam-3759	111	14	m	m	VERB
ejpam-3759	111	15	r	r	NOUN
ejpam-3759	111	16	{	{	PUNCT
ejpam-3759	111	17	m	m	VERB
ejpam-3759	111	18	}	}	PUNCT
ejpam-3759	111	19	is	be	AUX
ejpam-3759	111	20	an	an	DET
ejpam-3759	111	21	almost	almost	ADV
ejpam-3759	111	22	bi	bi	ADJ
ejpam-3759	111	23	-	-	ADJ
ejpam-3759	111	24	γ	γ	NOUN
ejpam-3759	111	25	-	-	NOUN
ejpam-3759	111	26	ideal	ideal	NOUN
ejpam-3759	111	27	of	of	ADP
ejpam-3759	111	28	m	m	PRON
ejpam-3759	111	29	by	by	ADP
ejpam-3759	111	30	theorem	theorem	NOUN
ejpam-3759	111	31	1	1	NUM
ejpam-3759	111	32	.	.	PUNCT
ejpam-3759	112	1	this	this	PRON
ejpam-3759	112	2	implies	imply	VERB
ejpam-3759	112	3	that	that	SCONJ
ejpam-3759	112	4	∅	∅	NOUN
ejpam-3759	112	5	=	=	PUNCT
ejpam-3759	112	6	{	{	PUNCT
ejpam-3759	112	7	m	m	NOUN
ejpam-3759	112	8	}	}	PUNCT
ejpam-3759	112	9	∩	∩	NOUN
ejpam-3759	112	10	(	(	PUNCT
ejpam-3759	112	11	m	m	PROPN
ejpam-3759	112	12	r	r	NOUN
ejpam-3759	112	13	{	{	PUNCT
ejpam-3759	112	14	m	m	NOUN
ejpam-3759	112	15	}	}	PUNCT
ejpam-3759	112	16	)	)	PUNCT
ejpam-3759	113	1	=	=	SYM
ejpam-3759	113	2	(	(	PUNCT
ejpam-3759	113	3	m	m	VERB
ejpam-3759	113	4	r	r	NOUN
ejpam-3759	113	5	{	{	PUNCT
ejpam-3759	113	6	m})γaγ(m	m})γaγ(m	NOUN
ejpam-3759	113	7	r	r	NOUN
ejpam-3759	113	8	{	{	PUNCT
ejpam-3759	113	9	m})∩	m})∩	PROPN
ejpam-3759	113	10	(	(	PUNCT
ejpam-3759	113	11	m	m	NOUN
ejpam-3759	113	12	r	r	NOUN
ejpam-3759	113	13	{	{	PUNCT
ejpam-3759	113	14	m	m	NOUN
ejpam-3759	113	15	}	}	PUNCT
ejpam-3759	113	16	)	)	PUNCT
ejpam-3759	113	17	6=	6=	ADP
ejpam-3759	113	18	∅	∅	NOUN
ejpam-3759	113	19	,	,	PUNCT
ejpam-3759	113	20	which	which	PRON
ejpam-3759	113	21	is	be	AUX
ejpam-3759	113	22	a	a	DET
ejpam-3759	113	23	contradiction	contradiction	NOUN
ejpam-3759	113	24	.	.	PUNCT
ejpam-3759	114	1	therefore	therefore	ADV
ejpam-3759	114	2	,	,	PUNCT
ejpam-3759	114	3	m	m	VERB
ejpam-3759	114	4	has	have	VERB
ejpam-3759	114	5	no	no	DET
ejpam-3759	114	6	proper	proper	ADJ
ejpam-3759	114	7	almost	almost	ADV
ejpam-3759	114	8	bi	bi	ADJ
ejpam-3759	114	9	-	-	ADJ
ejpam-3759	114	10	γ	γ	NOUN
ejpam-3759	114	11	-	-	NOUN
ejpam-3759	114	12	ideals	ideal	NOUN
ejpam-3759	114	13	.	.	PUNCT
ejpam-3759	115	1	3	3	X
ejpam-3759	115	2	.	.	X
ejpam-3759	115	3	fuzzy	fuzzy	ADJ
ejpam-3759	115	4	almost	almost	ADV
ejpam-3759	115	5	bi	bi	ADJ
ejpam-3759	115	6	-	-	ADJ
ejpam-3759	115	7	γ	γ	NOUN
ejpam-3759	115	8	-	-	PUNCT
ejpam-3759	115	9	ideals	ideal	NOUN
ejpam-3759	115	10	for	for	ADP
ejpam-3759	115	11	a	a	DET
ejpam-3759	115	12	γ	γ	NOUN
ejpam-3759	115	13	-	-	PUNCT
ejpam-3759	115	14	semigroup	semigroup	NOUN
ejpam-3759	115	15	m	m	VERB
ejpam-3759	115	16	,	,	PUNCT
ejpam-3759	115	17	let	let	VERB
ejpam-3759	115	18	f(m	f(m	PROPN
ejpam-3759	115	19	)	)	PUNCT
ejpam-3759	115	20	be	be	VERB
ejpam-3759	115	21	the	the	DET
ejpam-3759	115	22	set	set	NOUN
ejpam-3759	115	23	of	of	ADP
ejpam-3759	115	24	all	all	DET
ejpam-3759	115	25	fuzzy	fuzzy	ADJ
ejpam-3759	115	26	subsets	subset	NOUN
ejpam-3759	115	27	of	of	ADP
ejpam-3759	115	28	m	m	PROPN
ejpam-3759	115	29	.	.	PUNCT
ejpam-3759	116	1	for	for	ADP
ejpam-3759	116	2	each	each	DET
ejpam-3759	116	3	α	α	PROPN
ejpam-3759	116	4	∈	∈	PROPN
ejpam-3759	116	5	γ	γ	X
ejpam-3759	116	6	,	,	PUNCT
ejpam-3759	116	7	define	define	VERB
ejpam-3759	116	8	a	a	DET
ejpam-3759	116	9	binary	binary	ADJ
ejpam-3759	116	10	operation	operation	NOUN
ejpam-3759	116	11	◦	◦	NOUN
ejpam-3759	116	12	α	α	NOUN
ejpam-3759	116	13	on	on	ADP
ejpam-3759	116	14	f(m	f(m	PROPN
ejpam-3759	116	15	)	)	PUNCT
ejpam-3759	116	16	by	by	ADP
ejpam-3759	116	17	(	(	PUNCT
ejpam-3759	116	18	f	f	PROPN
ejpam-3759	116	19	◦	◦	NOUN
ejpam-3759	116	20	α	α	NOUN
ejpam-3759	116	21	g)(m	g)(m	NOUN
ejpam-3759	116	22	)	)	PUNCT
ejpam-3759	116	23	=	=	PUNCT
ejpam-3759	117	1			PUNCT
ejpam-3759	117	2	sup	sup	NOUN
ejpam-3759	117	3	m	m	NOUN
ejpam-3759	117	4	=	=	NOUN
ejpam-3759	117	5	aαb	aαb	NOUN
ejpam-3759	117	6	{	{	PUNCT
ejpam-3759	117	7	min{f(a	min{f(a	PROPN
ejpam-3759	117	8	)	)	PUNCT
ejpam-3759	117	9	,	,	PUNCT
ejpam-3759	117	10	g(b	g(b	PROPN
ejpam-3759	117	11	)	)	PUNCT
ejpam-3759	117	12	}	}	PUNCT
ejpam-3759	117	13	}	}	PUNCT
ejpam-3759	117	14	if	if	SCONJ
ejpam-3759	117	15	m	m	ADJ
ejpam-3759	117	16	∈mαm	∈mαm	NOUN
ejpam-3759	117	17	,	,	PUNCT
ejpam-3759	117	18	0	0	NUM
ejpam-3759	117	19	otherwise	otherwise	ADV
ejpam-3759	117	20	.	.	PUNCT
ejpam-3759	118	1	let	let	VERB
ejpam-3759	118	2	γ	γ	X
ejpam-3759	118	3	?	?	PUNCT
ejpam-3759	119	1	:	:	PUNCT
ejpam-3759	119	2	=	=	PRON
ejpam-3759	119	3	{	{	PUNCT
ejpam-3759	119	4	◦	◦	NOUN
ejpam-3759	119	5	α	α	NOUN
ejpam-3759	119	6	|	|	ADV
ejpam-3759	119	7	α	α	NOUN
ejpam-3759	119	8	∈	∈	PROPN
ejpam-3759	119	9	γ	γ	X
ejpam-3759	119	10	}	}	PUNCT
ejpam-3759	119	11	.	.	PUNCT
ejpam-3759	120	1	then	then	ADV
ejpam-3759	120	2	(	(	PUNCT
ejpam-3759	120	3	f(m),γ	f(m),γ	PROPN
ejpam-3759	120	4	?	?	PUNCT
ejpam-3759	120	5	)	)	PUNCT
ejpam-3759	120	6	is	be	AUX
ejpam-3759	120	7	a	a	DET
ejpam-3759	120	8	γ	γ	NOUN
ejpam-3759	120	9	-	-	PUNCT
ejpam-3759	120	10	semigroup	semigroup	NOUN
ejpam-3759	120	11	.	.	PUNCT
ejpam-3759	121	1	proposition	proposition	NOUN
ejpam-3759	121	2	1	1	NUM
ejpam-3759	121	3	.	.	PUNCT
ejpam-3759	122	1	for	for	ADP
ejpam-3759	122	2	fuzzy	fuzzy	ADJ
ejpam-3759	122	3	subsets	subset	NOUN
ejpam-3759	122	4	f	f	PROPN
ejpam-3759	122	5	and	and	CCONJ
ejpam-3759	122	6	g	g	PROPN
ejpam-3759	122	7	of	of	ADP
ejpam-3759	122	8	a	a	DET
ejpam-3759	122	9	γ	γ	NOUN
ejpam-3759	122	10	-	-	PUNCT
ejpam-3759	122	11	semigroup	semigroup	NOUN
ejpam-3759	122	12	m	m	VERB
ejpam-3759	123	1	such	such	ADJ
ejpam-3759	123	2	that	that	SCONJ
ejpam-3759	123	3	f	f	PROPN
ejpam-3759	123	4	⊆	⊆	NUM
ejpam-3759	123	5	g	g	NOUN
ejpam-3759	123	6	and	and	CCONJ
ejpam-3759	123	7	α	α	PRON
ejpam-3759	123	8	∈	∈	PROPN
ejpam-3759	123	9	γ	γ	X
ejpam-3759	123	10	,	,	PUNCT
ejpam-3759	123	11	if	if	SCONJ
ejpam-3759	123	12	h	h	NOUN
ejpam-3759	123	13	is	be	AUX
ejpam-3759	123	14	any	any	DET
ejpam-3759	123	15	fuzzy	fuzzy	ADJ
ejpam-3759	123	16	subset	subset	NOUN
ejpam-3759	123	17	of	of	ADP
ejpam-3759	123	18	m	m	PROPN
ejpam-3759	123	19	,	,	PUNCT
ejpam-3759	123	20	then	then	ADV
ejpam-3759	123	21	h	h	PROPN
ejpam-3759	123	22	◦	◦	NOUN
ejpam-3759	123	23	α	α	NOUN
ejpam-3759	123	24	f	f	NOUN
ejpam-3759	123	25	⊆	⊆	NUM
ejpam-3759	123	26	h	h	NOUN
ejpam-3759	123	27	◦	◦	NOUN
ejpam-3759	123	28	α	α	NOUN
ejpam-3759	123	29	g	g	NOUN
ejpam-3759	123	30	and	and	CCONJ
ejpam-3759	123	31	f	f	PROPN
ejpam-3759	123	32	◦	◦	NOUN
ejpam-3759	123	33	α	α	NOUN
ejpam-3759	123	34	h	h	NOUN
ejpam-3759	123	35	⊆	⊆	NUM
ejpam-3759	123	36	g	g	NOUN
ejpam-3759	123	37	◦	◦	PROPN
ejpam-3759	123	38	α	α	PROPN
ejpam-3759	123	39	h.	h.	PROPN
ejpam-3759	123	40	r.	r.	PROPN
ejpam-3759	123	41	chinram	chinram	PROPN
ejpam-3759	123	42	et	et	PROPN
ejpam-3759	123	43	al	al	PROPN
ejpam-3759	123	44	.	.	PUNCT
ejpam-3759	123	45	/	/	SYM
ejpam-3759	123	46	eur	eur	PROPN
ejpam-3759	123	47	.	.	PUNCT
ejpam-3759	124	1	j.	j.	PROPN
ejpam-3759	124	2	pure	pure	PROPN
ejpam-3759	124	3	appl	appl	PROPN
ejpam-3759	124	4	.	.	PROPN
ejpam-3759	124	5	math	math	PROPN
ejpam-3759	124	6	,	,	PUNCT
ejpam-3759	124	7	13	13	NUM
ejpam-3759	124	8	(	(	PUNCT
ejpam-3759	124	9	3	3	NUM
ejpam-3759	124	10	)	)	PUNCT
ejpam-3759	124	11	(	(	PUNCT
ejpam-3759	124	12	2020	2020	NUM
ejpam-3759	124	13	)	)	PUNCT
ejpam-3759	124	14	,	,	PUNCT
ejpam-3759	124	15	620	620	NUM
ejpam-3759	124	16	-	-	SYM
ejpam-3759	124	17	630	630	NUM
ejpam-3759	124	18	625	625	NUM
ejpam-3759	124	19	we	we	PRON
ejpam-3759	124	20	define	define	VERB
ejpam-3759	124	21	fuzzification	fuzzification	NOUN
ejpam-3759	124	22	of	of	ADP
ejpam-3759	124	23	almost	almost	ADV
ejpam-3759	124	24	bi	bi	ADJ
ejpam-3759	124	25	-	-	ADJ
ejpam-3759	124	26	γ	γ	NOUN
ejpam-3759	124	27	-	-	PUNCT
ejpam-3759	124	28	ideals	ideal	NOUN
ejpam-3759	124	29	in	in	ADP
ejpam-3759	124	30	γ	γ	NOUN
ejpam-3759	124	31	-	-	PUNCT
ejpam-3759	124	32	semigroups	semigroup	NOUN
ejpam-3759	124	33	as	as	SCONJ
ejpam-3759	124	34	follows	follow	VERB
ejpam-3759	124	35	:	:	PUNCT
ejpam-3759	124	36	definition	definition	NOUN
ejpam-3759	124	37	4	4	NUM
ejpam-3759	124	38	.	.	PUNCT
ejpam-3759	125	1	a	a	DET
ejpam-3759	125	2	fuzzy	fuzzy	ADJ
ejpam-3759	125	3	subset	subset	NOUN
ejpam-3759	125	4	f	f	PROPN
ejpam-3759	125	5	of	of	ADP
ejpam-3759	125	6	a	a	DET
ejpam-3759	125	7	γ	γ	PROPN
ejpam-3759	125	8	-	-	PUNCT
ejpam-3759	125	9	semigroup	semigroup	NOUN
ejpam-3759	125	10	m	m	VERB
ejpam-3759	125	11	is	be	AUX
ejpam-3759	125	12	called	call	VERB
ejpam-3759	125	13	a	a	DET
ejpam-3759	125	14	fuzzy	fuzzy	ADJ
ejpam-3759	125	15	almost	almost	ADV
ejpam-3759	125	16	bi	bi	ADJ
ejpam-3759	125	17	-	-	ADJ
ejpam-3759	125	18	γ	γ	NOUN
ejpam-3759	125	19	-	-	NOUN
ejpam-3759	125	20	ideal	ideal	NOUN
ejpam-3759	125	21	of	of	ADP
ejpam-3759	125	22	m	m	PRON
ejpam-3759	125	23	if	if	SCONJ
ejpam-3759	125	24	for	for	ADP
ejpam-3759	125	25	all	all	DET
ejpam-3759	125	26	fuzzy	fuzzy	ADJ
ejpam-3759	125	27	points	point	NOUN
ejpam-3759	125	28	mt	mt	PROPN
ejpam-3759	125	29	of	of	ADP
ejpam-3759	125	30	m	m	PROPN
ejpam-3759	125	31	,	,	PUNCT
ejpam-3759	125	32	there	there	PRON
ejpam-3759	125	33	exist	exist	VERB
ejpam-3759	125	34	α	α	PRON
ejpam-3759	125	35	,	,	PUNCT
ejpam-3759	125	36	β	β	X
ejpam-3759	125	37	∈	∈	PROPN
ejpam-3759	125	38	γ	γ	NOUN
ejpam-3759	125	39	such	such	ADJ
ejpam-3759	125	40	that	that	PRON
ejpam-3759	125	41	(	(	PUNCT
ejpam-3759	125	42	f	f	PROPN
ejpam-3759	125	43	◦	◦	PROPN
ejpam-3759	125	44	α	α	PROPN
ejpam-3759	125	45	mt	mt	PROPN
ejpam-3759	125	46	◦	◦	PROPN
ejpam-3759	125	47	β	β	X
ejpam-3759	125	48	f	f	NOUN
ejpam-3759	125	49	)	)	PUNCT
ejpam-3759	125	50	∩	∩	PROPN
ejpam-3759	125	51	f	f	PROPN
ejpam-3759	125	52	6=	6=	PROPN
ejpam-3759	125	53	0	0	NUM
ejpam-3759	125	54	.	.	PUNCT
ejpam-3759	126	1	theorem	theorem	NOUN
ejpam-3759	126	2	4	4	NUM
ejpam-3759	126	3	.	.	PUNCT
ejpam-3759	127	1	assume	assume	VERB
ejpam-3759	127	2	that	that	SCONJ
ejpam-3759	127	3	f	f	PROPN
ejpam-3759	127	4	and	and	CCONJ
ejpam-3759	127	5	g	g	PROPN
ejpam-3759	127	6	are	be	AUX
ejpam-3759	127	7	fuzzy	fuzzy	ADJ
ejpam-3759	127	8	subsets	subset	NOUN
ejpam-3759	127	9	of	of	ADP
ejpam-3759	127	10	a	a	DET
ejpam-3759	127	11	γ	γ	NOUN
ejpam-3759	127	12	-	-	PUNCT
ejpam-3759	127	13	semigroup	semigroup	NOUN
ejpam-3759	127	14	m	m	VERB
ejpam-3759	127	15	such	such	ADJ
ejpam-3759	127	16	that	that	SCONJ
ejpam-3759	127	17	f	f	PROPN
ejpam-3759	127	18	⊆	⊆	NUM
ejpam-3759	127	19	g.	g.	NOUN
ejpam-3759	127	20	if	if	SCONJ
ejpam-3759	127	21	f	f	PROPN
ejpam-3759	127	22	is	be	AUX
ejpam-3759	127	23	a	a	DET
ejpam-3759	127	24	fuzzy	fuzzy	ADJ
ejpam-3759	127	25	almost	almost	ADV
ejpam-3759	127	26	bi	bi	ADJ
ejpam-3759	127	27	-	-	ADJ
ejpam-3759	127	28	γ	γ	NOUN
ejpam-3759	127	29	-	-	NOUN
ejpam-3759	127	30	ideal	ideal	NOUN
ejpam-3759	127	31	of	of	ADP
ejpam-3759	127	32	m	m	PROPN
ejpam-3759	127	33	,	,	PUNCT
ejpam-3759	127	34	then	then	ADV
ejpam-3759	127	35	g	g	PROPN
ejpam-3759	127	36	is	be	AUX
ejpam-3759	127	37	also	also	ADV
ejpam-3759	127	38	a	a	DET
ejpam-3759	127	39	fuzzy	fuzzy	ADJ
ejpam-3759	127	40	almost	almost	ADV
ejpam-3759	127	41	bi	bi	ADJ
ejpam-3759	127	42	-	-	ADJ
ejpam-3759	127	43	γ	γ	NOUN
ejpam-3759	127	44	-	-	NOUN
ejpam-3759	127	45	ideal	ideal	NOUN
ejpam-3759	127	46	of	of	ADP
ejpam-3759	127	47	m	m	PROPN
ejpam-3759	127	48	.	.	PUNCT
ejpam-3759	128	1	proof	proof	NOUN
ejpam-3759	128	2	.	.	PUNCT
ejpam-3759	129	1	since	since	SCONJ
ejpam-3759	129	2	f	f	PROPN
ejpam-3759	129	3	is	be	AUX
ejpam-3759	129	4	a	a	DET
ejpam-3759	129	5	fuzzy	fuzzy	ADJ
ejpam-3759	129	6	almost	almost	ADV
ejpam-3759	129	7	bi	bi	ADJ
ejpam-3759	129	8	-	-	ADJ
ejpam-3759	129	9	γ	γ	NOUN
ejpam-3759	129	10	-	-	NOUN
ejpam-3759	129	11	ideal	ideal	NOUN
ejpam-3759	129	12	of	of	ADP
ejpam-3759	129	13	m	m	PRON
ejpam-3759	129	14	,	,	PUNCT
ejpam-3759	129	15	for	for	ADP
ejpam-3759	129	16	each	each	DET
ejpam-3759	129	17	fuzzy	fuzzy	ADJ
ejpam-3759	129	18	point	point	NOUN
ejpam-3759	129	19	mt	mt	PROPN
ejpam-3759	129	20	of	of	ADP
ejpam-3759	129	21	m	m	PROPN
ejpam-3759	129	22	,	,	PUNCT
ejpam-3759	129	23	there	there	PRON
ejpam-3759	129	24	exist	exist	VERB
ejpam-3759	129	25	α	α	PRON
ejpam-3759	129	26	,	,	PUNCT
ejpam-3759	129	27	β	β	X
ejpam-3759	129	28	∈	∈	PROPN
ejpam-3759	129	29	γ	γ	NOUN
ejpam-3759	129	30	such	such	ADJ
ejpam-3759	129	31	that	that	PRON
ejpam-3759	129	32	(	(	PUNCT
ejpam-3759	129	33	f	f	PROPN
ejpam-3759	129	34	◦	◦	PROPN
ejpam-3759	129	35	α	α	PROPN
ejpam-3759	129	36	mt	mt	PROPN
ejpam-3759	129	37	◦	◦	PROPN
ejpam-3759	129	38	β	β	X
ejpam-3759	129	39	f	f	NOUN
ejpam-3759	129	40	)	)	PUNCT
ejpam-3759	129	41	∩	∩	PROPN
ejpam-3759	129	42	f	f	PROPN
ejpam-3759	129	43	6=	6=	PROPN
ejpam-3759	129	44	0	0	NUM
ejpam-3759	129	45	.	.	PUNCT
ejpam-3759	130	1	we	we	PRON
ejpam-3759	130	2	have	have	VERB
ejpam-3759	130	3	that	that	PRON
ejpam-3759	130	4	(	(	PUNCT
ejpam-3759	130	5	f	f	PROPN
ejpam-3759	130	6	◦	◦	PROPN
ejpam-3759	130	7	α	α	PROPN
ejpam-3759	130	8	mt	mt	PROPN
ejpam-3759	130	9	◦	◦	PROPN
ejpam-3759	130	10	β	β	X
ejpam-3759	130	11	f	f	NOUN
ejpam-3759	130	12	)	)	PUNCT
ejpam-3759	130	13	∩	∩	NOUN
ejpam-3759	130	14	f	f	PROPN
ejpam-3759	130	15	⊆	⊆	NUM
ejpam-3759	130	16	(	(	PUNCT
ejpam-3759	130	17	g	g	NOUN
ejpam-3759	130	18	◦	◦	NOUN
ejpam-3759	130	19	αmt	αmt	NOUN
ejpam-3759	130	20	◦	◦	NOUN
ejpam-3759	130	21	β	β	NOUN
ejpam-3759	130	22	g	g	NOUN
ejpam-3759	130	23	)	)	PUNCT
ejpam-3759	130	24	∩	∩	PROPN
ejpam-3759	130	25	g	g	PROPN
ejpam-3759	130	26	,	,	PUNCT
ejpam-3759	130	27	this	this	PRON
ejpam-3759	130	28	implies	imply	VERB
ejpam-3759	130	29	that	that	SCONJ
ejpam-3759	130	30	(	(	PUNCT
ejpam-3759	130	31	g	g	NOUN
ejpam-3759	130	32	◦	◦	NOUN
ejpam-3759	130	33	αmt	αmt	NOUN
ejpam-3759	130	34	◦	◦	NOUN
ejpam-3759	130	35	β	β	NOUN
ejpam-3759	130	36	g	g	NOUN
ejpam-3759	130	37	)	)	PUNCT
ejpam-3759	130	38	∩	∩	NOUN
ejpam-3759	130	39	g	g	PROPN
ejpam-3759	130	40	6=	6=	PROPN
ejpam-3759	130	41	0	0	NUM
ejpam-3759	130	42	.	.	PUNCT
ejpam-3759	131	1	hence	hence	ADV
ejpam-3759	131	2	,	,	PUNCT
ejpam-3759	131	3	g	g	PROPN
ejpam-3759	131	4	is	be	AUX
ejpam-3759	131	5	also	also	ADV
ejpam-3759	131	6	a	a	DET
ejpam-3759	131	7	fuzzy	fuzzy	ADJ
ejpam-3759	131	8	almost	almost	ADV
ejpam-3759	131	9	bi	bi	ADJ
ejpam-3759	131	10	-	-	ADJ
ejpam-3759	131	11	γ	γ	NOUN
ejpam-3759	131	12	-	-	NOUN
ejpam-3759	131	13	ideal	ideal	NOUN
ejpam-3759	131	14	of	of	ADP
ejpam-3759	131	15	m	m	PROPN
ejpam-3759	131	16	.	.	PUNCT
ejpam-3759	132	1	corollary	corollary	ADJ
ejpam-3759	132	2	2	2	NUM
ejpam-3759	132	3	.	.	PUNCT
ejpam-3759	133	1	if	if	SCONJ
ejpam-3759	133	2	f	f	PROPN
ejpam-3759	133	3	and	and	CCONJ
ejpam-3759	133	4	g	g	PROPN
ejpam-3759	133	5	are	be	AUX
ejpam-3759	133	6	fuzzy	fuzzy	ADJ
ejpam-3759	133	7	almost	almost	ADV
ejpam-3759	133	8	bi	bi	ADJ
ejpam-3759	133	9	-	-	ADJ
ejpam-3759	133	10	γ	γ	NOUN
ejpam-3759	133	11	-	-	PUNCT
ejpam-3759	133	12	ideals	ideal	NOUN
ejpam-3759	133	13	of	of	ADP
ejpam-3759	133	14	a	a	DET
ejpam-3759	133	15	γ	γ	NOUN
ejpam-3759	133	16	-	-	PUNCT
ejpam-3759	133	17	semigroup	semigroup	NOUN
ejpam-3759	133	18	m	m	NOUN
ejpam-3759	133	19	,	,	PUNCT
ejpam-3759	133	20	then	then	ADV
ejpam-3759	133	21	f	f	PROPN
ejpam-3759	133	22	∪	∪	PROPN
ejpam-3759	133	23	g	g	PROPN
ejpam-3759	133	24	is	be	AUX
ejpam-3759	133	25	also	also	ADV
ejpam-3759	133	26	a	a	DET
ejpam-3759	133	27	fuzzy	fuzzy	ADJ
ejpam-3759	133	28	almost	almost	ADV
ejpam-3759	133	29	bi	bi	ADJ
ejpam-3759	133	30	-	-	ADJ
ejpam-3759	133	31	γ	γ	NOUN
ejpam-3759	133	32	-	-	NOUN
ejpam-3759	133	33	ideal	ideal	NOUN
ejpam-3759	133	34	of	of	ADP
ejpam-3759	133	35	m	m	PROPN
ejpam-3759	133	36	.	.	PUNCT
ejpam-3759	134	1	proof	proof	NOUN
ejpam-3759	134	2	.	.	PUNCT
ejpam-3759	135	1	it	it	PRON
ejpam-3759	135	2	follows	follow	VERB
ejpam-3759	135	3	by	by	ADP
ejpam-3759	135	4	theorem	theorem	NOUN
ejpam-3759	135	5	4	4	NUM
ejpam-3759	135	6	because	because	SCONJ
ejpam-3759	135	7	of	of	ADP
ejpam-3759	135	8	f	f	PROPN
ejpam-3759	135	9	⊆	⊆	NUM
ejpam-3759	135	10	f	f	PROPN
ejpam-3759	135	11	∪	∪	PROPN
ejpam-3759	135	12	g.	g.	PROPN
ejpam-3759	135	13	example	example	NOUN
ejpam-3759	135	14	5	5	NUM
ejpam-3759	135	15	.	.	X
ejpam-3759	135	16	consider	consider	VERB
ejpam-3759	135	17	the	the	DET
ejpam-3759	135	18	γ	γ	NOUN
ejpam-3759	135	19	-	-	PUNCT
ejpam-3759	135	20	semigroup	semigroup	ADJ
ejpam-3759	135	21	z5	z5	NOUN
ejpam-3759	135	22	where	where	SCONJ
ejpam-3759	135	23	γ	γ	X
ejpam-3759	135	24	=	=	SYM
ejpam-3759	135	25	{	{	PUNCT
ejpam-3759	135	26	0	0	NUM
ejpam-3759	135	27	}	}	PUNCT
ejpam-3759	135	28	and	and	CCONJ
ejpam-3759	135	29	aγb	aγb	VERB
ejpam-3759	135	30	:	:	PUNCT
ejpam-3759	135	31	=	=	PUNCT
ejpam-3759	135	32	a	a	PRON
ejpam-3759	135	33	+	+	X
ejpam-3759	135	34	γ	γ	X
ejpam-3759	135	35	+	+	PROPN
ejpam-3759	135	36	b.	b.	PROPN
ejpam-3759	135	37	let	let	VERB
ejpam-3759	135	38	f	f	PROPN
ejpam-3759	135	39	and	and	CCONJ
ejpam-3759	135	40	g	g	PROPN
ejpam-3759	135	41	be	be	VERB
ejpam-3759	135	42	fuzzy	fuzzy	ADJ
ejpam-3759	135	43	subsets	subset	NOUN
ejpam-3759	135	44	of	of	ADP
ejpam-3759	135	45	z5	z5	NOUN
ejpam-3759	135	46	defined	define	VERB
ejpam-3759	135	47	by	by	ADP
ejpam-3759	135	48	f(0	f(0	NOUN
ejpam-3759	135	49	)	)	PUNCT
ejpam-3759	135	50	=	=	SYM
ejpam-3759	135	51	0	0	NUM
ejpam-3759	135	52	,	,	PUNCT
ejpam-3759	135	53	f(1	f(1	PROPN
ejpam-3759	135	54	)	)	PUNCT
ejpam-3759	135	55	=	=	NOUN
ejpam-3759	135	56	0.5	0.5	NUM
ejpam-3759	135	57	,	,	PUNCT
ejpam-3759	135	58	f(2	f(2	PROPN
ejpam-3759	135	59	)	)	PUNCT
ejpam-3759	135	60	=	=	SYM
ejpam-3759	135	61	0	0	NUM
ejpam-3759	135	62	,	,	PUNCT
ejpam-3759	135	63	f(3	f(3	PROPN
ejpam-3759	135	64	)	)	PUNCT
ejpam-3759	135	65	=	=	NOUN
ejpam-3759	135	66	0.1	0.1	NUM
ejpam-3759	135	67	,	,	PUNCT
ejpam-3759	135	68	f(4	f(4	PROPN
ejpam-3759	135	69	)	)	PUNCT
ejpam-3759	135	70	=	=	NOUN
ejpam-3759	135	71	0.4	0.4	NUM
ejpam-3759	135	72	and	and	CCONJ
ejpam-3759	135	73	g(0	g(0	PROPN
ejpam-3759	135	74	)	)	PUNCT
ejpam-3759	135	75	=	=	SYM
ejpam-3759	135	76	0	0	NUM
ejpam-3759	135	77	,	,	PUNCT
ejpam-3759	135	78	g(1	g(1	NOUN
ejpam-3759	135	79	)	)	PUNCT
ejpam-3759	135	80	=	=	SYM
ejpam-3759	135	81	0.3	0.3	NUM
ejpam-3759	135	82	,	,	PUNCT
ejpam-3759	135	83	g(2	g(2	PROPN
ejpam-3759	135	84	)	)	PUNCT
ejpam-3759	135	85	=	=	SYM
ejpam-3759	135	86	0.7	0.7	NUM
ejpam-3759	135	87	,	,	PUNCT
ejpam-3759	135	88	g(3	g(3	PROPN
ejpam-3759	135	89	)	)	PUNCT
ejpam-3759	135	90	=	=	SYM
ejpam-3759	135	91	0	0	NUM
ejpam-3759	135	92	,	,	PUNCT
ejpam-3759	135	93	g(4	g(4	NOUN
ejpam-3759	135	94	)	)	PUNCT
ejpam-3759	135	95	=	=	PUNCT
ejpam-3759	135	96	0.2	0.2	NUM
ejpam-3759	135	97	.	.	PUNCT
ejpam-3759	136	1	it	it	PRON
ejpam-3759	136	2	is	be	AUX
ejpam-3759	136	3	easy	easy	ADJ
ejpam-3759	136	4	to	to	PART
ejpam-3759	136	5	check	check	VERB
ejpam-3759	136	6	that	that	SCONJ
ejpam-3759	136	7	[	[	X
ejpam-3759	136	8	(	(	PUNCT
ejpam-3759	136	9	f	f	PROPN
ejpam-3759	136	10	◦	◦	PROPN
ejpam-3759	136	11	α	α	PROPN
ejpam-3759	136	12	mt	mt	PROPN
ejpam-3759	136	13	◦	◦	PROPN
ejpam-3759	136	14	β	β	X
ejpam-3759	136	15	f	f	NOUN
ejpam-3759	136	16	)	)	PUNCT
ejpam-3759	136	17	∩	∩	PROPN
ejpam-3759	136	18	f	f	X
ejpam-3759	136	19	]	]	X
ejpam-3759	136	20	(	(	PUNCT
ejpam-3759	136	21	4	4	NUM
ejpam-3759	136	22	)	)	PUNCT
ejpam-3759	136	23	6=	6=	ADP
ejpam-3759	136	24	0	0	NUM
ejpam-3759	137	1	and	and	CCONJ
ejpam-3759	137	2	[	[	X
ejpam-3759	137	3	(	(	PUNCT
ejpam-3759	137	4	g	g	PROPN
ejpam-3759	137	5	◦	◦	PROPN
ejpam-3759	137	6	α	α	PROPN
ejpam-3759	137	7	mt	mt	PROPN
ejpam-3759	137	8	◦	◦	PROPN
ejpam-3759	137	9	β	β	NOUN
ejpam-3759	137	10	g	g	NOUN
ejpam-3759	137	11	)	)	PUNCT
ejpam-3759	137	12	∩	∩	ADJ
ejpam-3759	137	13	g](4	g](4	PROPN
ejpam-3759	137	14	)	)	PUNCT
ejpam-3759	137	15	6=	6=	ADP
ejpam-3759	137	16	0	0	NUM
ejpam-3759	137	17	for	for	ADP
ejpam-3759	137	18	all	all	DET
ejpam-3759	137	19	α	α	NOUN
ejpam-3759	137	20	,	,	PUNCT
ejpam-3759	137	21	β	β	PROPN
ejpam-3759	137	22	∈	∈	PROPN
ejpam-3759	137	23	γ	γ	X
ejpam-3759	137	24	,	,	PUNCT
ejpam-3759	137	25	m	m	PROPN
ejpam-3759	137	26	∈	∈	NOUN
ejpam-3759	137	27	z5	z5	NOUN
ejpam-3759	137	28	and	and	CCONJ
ejpam-3759	137	29	t	t	PROPN
ejpam-3759	137	30	∈	∈	PROPN
ejpam-3759	137	31	(	(	PUNCT
ejpam-3759	137	32	0	0	NUM
ejpam-3759	137	33	,	,	PUNCT
ejpam-3759	137	34	1	1	NUM
ejpam-3759	137	35	]	]	PUNCT
ejpam-3759	137	36	.	.	PUNCT
ejpam-3759	138	1	so	so	ADV
ejpam-3759	138	2	f	f	PROPN
ejpam-3759	138	3	and	and	CCONJ
ejpam-3759	138	4	g	g	PROPN
ejpam-3759	138	5	are	be	AUX
ejpam-3759	138	6	fuzzy	fuzzy	ADJ
ejpam-3759	138	7	almost	almost	ADV
ejpam-3759	138	8	bi	bi	ADJ
ejpam-3759	138	9	-	-	ADJ
ejpam-3759	138	10	γ	γ	NOUN
ejpam-3759	138	11	-	-	PUNCT
ejpam-3759	138	12	ideals	ideal	NOUN
ejpam-3759	138	13	of	of	ADP
ejpam-3759	138	14	z5	z5	PROPN
ejpam-3759	138	15	.	.	PUNCT
ejpam-3759	139	1	from	from	ADP
ejpam-3759	139	2	the	the	DET
ejpam-3759	139	3	definition	definition	NOUN
ejpam-3759	139	4	of	of	ADP
ejpam-3759	139	5	the	the	DET
ejpam-3759	139	6	intersection	intersection	NOUN
ejpam-3759	139	7	of	of	ADP
ejpam-3759	139	8	two	two	NUM
ejpam-3759	139	9	fuzzy	fuzzy	ADJ
ejpam-3759	139	10	subsets	subset	NOUN
ejpam-3759	139	11	,	,	PUNCT
ejpam-3759	139	12	we	we	PRON
ejpam-3759	139	13	have	have	VERB
ejpam-3759	139	14	(	(	PUNCT
ejpam-3759	139	15	f	f	PROPN
ejpam-3759	139	16	∩	∩	X
ejpam-3759	139	17	g)(0	g)(0	X
ejpam-3759	139	18	)	)	PUNCT
ejpam-3759	140	1	=	=	SYM
ejpam-3759	140	2	0	0	NUM
ejpam-3759	140	3	,	,	PUNCT
ejpam-3759	140	4	(	(	PUNCT
ejpam-3759	140	5	f	f	PROPN
ejpam-3759	140	6	∩	∩	NOUN
ejpam-3759	140	7	g)(1	g)(1	X
ejpam-3759	140	8	)	)	PUNCT
ejpam-3759	140	9	=	=	SYM
ejpam-3759	140	10	0.3	0.3	NUM
ejpam-3759	140	11	,	,	PUNCT
ejpam-3759	140	12	(	(	PUNCT
ejpam-3759	140	13	f	f	PROPN
ejpam-3759	140	14	∩	∩	NOUN
ejpam-3759	140	15	g)(2	g)(2	X
ejpam-3759	140	16	)	)	PUNCT
ejpam-3759	140	17	=	=	SYM
ejpam-3759	140	18	0	0	NUM
ejpam-3759	140	19	,	,	PUNCT
ejpam-3759	140	20	(	(	PUNCT
ejpam-3759	140	21	f	f	PROPN
ejpam-3759	140	22	∩	∩	NOUN
ejpam-3759	140	23	g)(3	g)(3	NOUN
ejpam-3759	140	24	)	)	PUNCT
ejpam-3759	140	25	=	=	SYM
ejpam-3759	140	26	0	0	NUM
ejpam-3759	140	27	,	,	PUNCT
ejpam-3759	140	28	(	(	PUNCT
ejpam-3759	140	29	f	f	PROPN
ejpam-3759	140	30	∩	∩	X
ejpam-3759	140	31	g)(4	g)(4	X
ejpam-3759	140	32	)	)	PUNCT
ejpam-3759	140	33	=	=	SYM
ejpam-3759	140	34	0.2	0.2	NUM
ejpam-3759	140	35	.	.	PUNCT
ejpam-3759	141	1	we	we	PRON
ejpam-3759	141	2	can	can	AUX
ejpam-3759	141	3	easily	easily	ADV
ejpam-3759	141	4	to	to	PART
ejpam-3759	141	5	check	check	VERB
ejpam-3759	141	6	that	that	PRON
ejpam-3759	141	7	[	[	X
ejpam-3759	141	8	(	(	PUNCT
ejpam-3759	141	9	(	(	PUNCT
ejpam-3759	141	10	f∩g)	f∩g)	PROPN
ejpam-3759	141	11	◦	◦	NOUN
ejpam-3759	141	12	α0t	α0t	NOUN
ejpam-3759	141	13	◦	◦	NOUN
ejpam-3759	141	14	β	β	X
ejpam-3759	141	15	(	(	PUNCT
ejpam-3759	141	16	f∩g))∩(f∩g)](a	f∩g))∩(f∩g)](a	PROPN
ejpam-3759	141	17	)	)	PUNCT
ejpam-3759	141	18	=	=	SYM
ejpam-3759	141	19	0	0	NUM
ejpam-3759	141	20	for	for	ADP
ejpam-3759	141	21	all	all	DET
ejpam-3759	141	22	α	α	NOUN
ejpam-3759	141	23	,	,	PUNCT
ejpam-3759	141	24	β	β	PROPN
ejpam-3759	141	25	∈	∈	PROPN
ejpam-3759	141	26	γ	γ	X
ejpam-3759	141	27	,	,	PUNCT
ejpam-3759	141	28	t	t	PROPN
ejpam-3759	141	29	∈	∈	PROPN
ejpam-3759	141	30	(	(	PUNCT
ejpam-3759	141	31	0	0	NUM
ejpam-3759	141	32	,	,	PUNCT
ejpam-3759	141	33	1	1	NUM
ejpam-3759	141	34	]	]	PUNCT
ejpam-3759	141	35	and	and	CCONJ
ejpam-3759	141	36	a	a	DET
ejpam-3759	141	37	∈	∈	PROPN
ejpam-3759	141	38	z5	z5	NOUN
ejpam-3759	141	39	,	,	PUNCT
ejpam-3759	141	40	so	so	SCONJ
ejpam-3759	141	41	f	f	PROPN
ejpam-3759	141	42	∩	∩	PROPN
ejpam-3759	141	43	g	g	PROPN
ejpam-3759	141	44	is	be	AUX
ejpam-3759	141	45	not	not	PART
ejpam-3759	141	46	a	a	DET
ejpam-3759	141	47	fuzzy	fuzzy	ADJ
ejpam-3759	141	48	almost	almost	ADV
ejpam-3759	141	49	bi	bi	ADJ
ejpam-3759	141	50	-	-	ADJ
ejpam-3759	141	51	γ	γ	NOUN
ejpam-3759	141	52	-	-	NOUN
ejpam-3759	141	53	ideal	ideal	NOUN
ejpam-3759	141	54	of	of	ADP
ejpam-3759	141	55	z5	z5	PROPN
ejpam-3759	141	56	.	.	PUNCT
ejpam-3759	142	1	the	the	DET
ejpam-3759	142	2	following	follow	VERB
ejpam-3759	142	3	remark	remark	NOUN
ejpam-3759	142	4	follows	follow	VERB
ejpam-3759	142	5	from	from	ADP
ejpam-3759	142	6	example	example	NOUN
ejpam-3759	142	7	5	5	NUM
ejpam-3759	142	8	.	.	PUNCT
ejpam-3759	142	9	remark	remark	NOUN
ejpam-3759	142	10	2	2	NUM
ejpam-3759	142	11	.	.	PUNCT
ejpam-3759	143	1	the	the	DET
ejpam-3759	143	2	intersection	intersection	NOUN
ejpam-3759	143	3	of	of	ADP
ejpam-3759	143	4	two	two	NUM
ejpam-3759	143	5	fuzzy	fuzzy	ADJ
ejpam-3759	143	6	almost	almost	ADV
ejpam-3759	143	7	bi	bi	ADJ
ejpam-3759	143	8	-	-	ADJ
ejpam-3759	143	9	γ	γ	NOUN
ejpam-3759	143	10	-	-	PUNCT
ejpam-3759	143	11	ideals	ideal	NOUN
ejpam-3759	143	12	of	of	ADP
ejpam-3759	143	13	a	a	DET
ejpam-3759	143	14	γ	γ	PROPN
ejpam-3759	143	15	-	-	PUNCT
ejpam-3759	143	16	semigroup	semigroup	NOUN
ejpam-3759	143	17	m	m	NOUN
ejpam-3759	143	18	need	need	AUX
ejpam-3759	143	19	not	not	PART
ejpam-3759	143	20	be	be	AUX
ejpam-3759	143	21	a	a	DET
ejpam-3759	143	22	fuzzy	fuzzy	ADJ
ejpam-3759	143	23	almost	almost	ADV
ejpam-3759	143	24	bi	bi	ADJ
ejpam-3759	143	25	-	-	ADJ
ejpam-3759	143	26	γ	γ	NOUN
ejpam-3759	143	27	-	-	NOUN
ejpam-3759	143	28	ideal	ideal	NOUN
ejpam-3759	143	29	of	of	ADP
ejpam-3759	143	30	m	m	PROPN
ejpam-3759	143	31	.	.	PUNCT
ejpam-3759	144	1	4	4	X
ejpam-3759	144	2	.	.	X
ejpam-3759	144	3	relationships	relationship	NOUN
ejpam-3759	144	4	between	between	ADP
ejpam-3759	144	5	almost	almost	ADV
ejpam-3759	144	6	bi	bi	NOUN
ejpam-3759	144	7	-	-	ADJ
ejpam-3759	144	8	γ	γ	NOUN
ejpam-3759	144	9	-	-	PUNCT
ejpam-3759	144	10	ideals	ideal	NOUN
ejpam-3759	144	11	and	and	CCONJ
ejpam-3759	144	12	their	their	PRON
ejpam-3759	144	13	fuzzification	fuzzification	NOUN
ejpam-3759	144	14	theorem	theorem	VERB
ejpam-3759	144	15	5	5	NUM
ejpam-3759	144	16	.	.	PUNCT
ejpam-3759	145	1	a	a	DET
ejpam-3759	145	2	non	non	ADJ
ejpam-3759	145	3	-	-	ADJ
ejpam-3759	145	4	empty	empty	ADJ
ejpam-3759	145	5	subset	subset	NOUN
ejpam-3759	145	6	b	b	NOUN
ejpam-3759	145	7	of	of	ADP
ejpam-3759	145	8	a	a	DET
ejpam-3759	145	9	γ	γ	PROPN
ejpam-3759	145	10	-	-	PUNCT
ejpam-3759	145	11	semigroup	semigroup	NOUN
ejpam-3759	145	12	m	m	VERB
ejpam-3759	145	13	is	be	AUX
ejpam-3759	145	14	an	an	DET
ejpam-3759	145	15	almost	almost	ADV
ejpam-3759	145	16	bi	bi	ADJ
ejpam-3759	145	17	-	-	ADJ
ejpam-3759	145	18	γ	γ	NOUN
ejpam-3759	145	19	-	-	NOUN
ejpam-3759	145	20	ideal	ideal	NOUN
ejpam-3759	145	21	of	of	ADP
ejpam-3759	145	22	m	m	PRON
ejpam-3759	145	23	if	if	SCONJ
ejpam-3759	146	1	and	and	CCONJ
ejpam-3759	146	2	only	only	ADV
ejpam-3759	146	3	if	if	SCONJ
ejpam-3759	146	4	χb	χb	PROPN
ejpam-3759	146	5	is	be	AUX
ejpam-3759	146	6	a	a	DET
ejpam-3759	146	7	fuzzy	fuzzy	ADJ
ejpam-3759	146	8	almost	almost	ADV
ejpam-3759	146	9	bi	bi	ADJ
ejpam-3759	146	10	-	-	ADJ
ejpam-3759	146	11	γ	γ	NOUN
ejpam-3759	146	12	-	-	NOUN
ejpam-3759	146	13	ideal	ideal	NOUN
ejpam-3759	146	14	of	of	ADP
ejpam-3759	146	15	m	m	PROPN
ejpam-3759	146	16	.	.	PUNCT
ejpam-3759	147	1	r.	r.	PROPN
ejpam-3759	147	2	chinram	chinram	PROPN
ejpam-3759	147	3	et	et	PROPN
ejpam-3759	147	4	al	al	PROPN
ejpam-3759	147	5	.	.	PUNCT
ejpam-3759	147	6	/	/	SYM
ejpam-3759	147	7	eur	eur	PROPN
ejpam-3759	147	8	.	.	PUNCT
ejpam-3759	148	1	j.	j.	PROPN
ejpam-3759	148	2	pure	pure	PROPN
ejpam-3759	148	3	appl	appl	PROPN
ejpam-3759	148	4	.	.	PROPN
ejpam-3759	148	5	math	math	PROPN
ejpam-3759	148	6	,	,	PUNCT
ejpam-3759	148	7	13	13	NUM
ejpam-3759	148	8	(	(	PUNCT
ejpam-3759	148	9	3	3	NUM
ejpam-3759	148	10	)	)	PUNCT
ejpam-3759	148	11	(	(	PUNCT
ejpam-3759	148	12	2020	2020	NUM
ejpam-3759	148	13	)	)	PUNCT
ejpam-3759	148	14	,	,	PUNCT
ejpam-3759	148	15	620	620	NUM
ejpam-3759	148	16	-	-	SYM
ejpam-3759	148	17	630	630	NUM
ejpam-3759	148	18	626	626	NUM
ejpam-3759	148	19	proof	proof	NOUN
ejpam-3759	148	20	.	.	PUNCT
ejpam-3759	149	1	assume	assume	VERB
ejpam-3759	149	2	that	that	SCONJ
ejpam-3759	149	3	b	b	PROPN
ejpam-3759	149	4	is	be	AUX
ejpam-3759	149	5	an	an	DET
ejpam-3759	149	6	almost	almost	ADV
ejpam-3759	149	7	bi	bi	ADJ
ejpam-3759	149	8	-	-	ADJ
ejpam-3759	149	9	γ	γ	NOUN
ejpam-3759	149	10	-	-	NOUN
ejpam-3759	149	11	ideal	ideal	NOUN
ejpam-3759	149	12	of	of	ADP
ejpam-3759	149	13	a	a	DET
ejpam-3759	149	14	γ	γ	NOUN
ejpam-3759	149	15	-	-	PUNCT
ejpam-3759	149	16	semigroup	semigroup	NOUN
ejpam-3759	149	17	m	m	NOUN
ejpam-3759	149	18	and	and	CCONJ
ejpam-3759	149	19	let	let	VERB
ejpam-3759	149	20	mt	mt	PROPN
ejpam-3759	149	21	be	be	AUX
ejpam-3759	149	22	any	any	DET
ejpam-3759	149	23	fuzzy	fuzzy	ADJ
ejpam-3759	149	24	point	point	NOUN
ejpam-3759	149	25	of	of	ADP
ejpam-3759	149	26	m	m	PROPN
ejpam-3759	149	27	.	.	PUNCT
ejpam-3759	150	1	then	then	ADV
ejpam-3759	150	2	bγmγb	bγmγb	PROPN
ejpam-3759	150	3	∩b	∩b	PROPN
ejpam-3759	150	4	6=	6=	ADP
ejpam-3759	150	5	∅.	∅.	VERB
ejpam-3759	150	6	thus	thus	ADV
ejpam-3759	150	7	there	there	PRON
ejpam-3759	150	8	exists	exist	VERB
ejpam-3759	150	9	b	b	PROPN
ejpam-3759	150	10	∈	∈	PROPN
ejpam-3759	150	11	b	b	NOUN
ejpam-3759	150	12	such	such	ADJ
ejpam-3759	150	13	that	that	DET
ejpam-3759	150	14	b	b	PROPN
ejpam-3759	150	15	∈	∈	PROPN
ejpam-3759	150	16	bαmβb	bαmβb	NOUN
ejpam-3759	150	17	for	for	ADP
ejpam-3759	150	18	some	some	DET
ejpam-3759	150	19	α	α	NOUN
ejpam-3759	150	20	,	,	PUNCT
ejpam-3759	150	21	β	β	PROPN
ejpam-3759	150	22	∈	∈	PROPN
ejpam-3759	150	23	γ	γ	X
ejpam-3759	150	24	.	.	PUNCT
ejpam-3759	151	1	this	this	PRON
ejpam-3759	151	2	implies	imply	VERB
ejpam-3759	151	3	that	that	SCONJ
ejpam-3759	151	4	(	(	PUNCT
ejpam-3759	151	5	χb	χb	AUX
ejpam-3759	151	6	◦	◦	NOUN
ejpam-3759	151	7	α	α	PROPN
ejpam-3759	151	8	mt	mt	PROPN
ejpam-3759	151	9	◦	◦	PROPN
ejpam-3759	151	10	β	β	X
ejpam-3759	151	11	χb)(b	χb)(b	PROPN
ejpam-3759	151	12	)	)	PUNCT
ejpam-3759	151	13	6=	6=	ADP
ejpam-3759	151	14	0	0	NUM
ejpam-3759	151	15	and	and	CCONJ
ejpam-3759	151	16	χb(b	χb(b	NOUN
ejpam-3759	151	17	)	)	PUNCT
ejpam-3759	151	18	6=	6=	ADP
ejpam-3759	151	19	0	0	NUM
ejpam-3759	151	20	.	.	PUNCT
ejpam-3759	152	1	hence	hence	ADV
ejpam-3759	152	2	,	,	PUNCT
ejpam-3759	152	3	(	(	PUNCT
ejpam-3759	152	4	χb	χb	ADP
ejpam-3759	152	5	◦	◦	NOUN
ejpam-3759	152	6	α	α	PROPN
ejpam-3759	152	7	mt	mt	PROPN
ejpam-3759	152	8	◦	◦	PROPN
ejpam-3759	152	9	β	β	X
ejpam-3759	152	10	χb	χb	NOUN
ejpam-3759	152	11	)	)	PUNCT
ejpam-3759	152	12	∩	∩	NOUN
ejpam-3759	152	13	χb	χb	ADP
ejpam-3759	152	14	6=	6=	PROPN
ejpam-3759	152	15	0	0	NUM
ejpam-3759	152	16	.	.	PUNCT
ejpam-3759	153	1	therefore	therefore	ADV
ejpam-3759	153	2	,	,	PUNCT
ejpam-3759	153	3	χb	χb	PROPN
ejpam-3759	153	4	is	be	AUX
ejpam-3759	153	5	a	a	DET
ejpam-3759	153	6	fuzzy	fuzzy	ADJ
ejpam-3759	153	7	almost	almost	ADV
ejpam-3759	153	8	bi	bi	ADJ
ejpam-3759	153	9	-	-	ADJ
ejpam-3759	153	10	γ	γ	NOUN
ejpam-3759	153	11	-	-	NOUN
ejpam-3759	153	12	ideal	ideal	NOUN
ejpam-3759	153	13	of	of	ADP
ejpam-3759	153	14	m	m	PROPN
ejpam-3759	153	15	.	.	PUNCT
ejpam-3759	154	1	to	to	PART
ejpam-3759	154	2	prove	prove	VERB
ejpam-3759	154	3	the	the	DET
ejpam-3759	154	4	converse	converse	NOUN
ejpam-3759	154	5	,	,	PUNCT
ejpam-3759	154	6	we	we	PRON
ejpam-3759	154	7	assume	assume	VERB
ejpam-3759	154	8	that	that	SCONJ
ejpam-3759	154	9	χb	χb	PROPN
ejpam-3759	154	10	is	be	AUX
ejpam-3759	154	11	a	a	DET
ejpam-3759	154	12	fuzzy	fuzzy	ADJ
ejpam-3759	154	13	almost	almost	ADV
ejpam-3759	154	14	bi	bi	ADJ
ejpam-3759	154	15	-	-	ADJ
ejpam-3759	154	16	γ	γ	NOUN
ejpam-3759	154	17	-	-	NOUN
ejpam-3759	154	18	ideal	ideal	NOUN
ejpam-3759	154	19	of	of	ADP
ejpam-3759	154	20	m	m	PRON
ejpam-3759	154	21	and	and	CCONJ
ejpam-3759	154	22	let	let	VERB
ejpam-3759	154	23	m	m	PRON
ejpam-3759	154	24	∈m	∈m	ADJ
ejpam-3759	154	25	.	.	PUNCT
ejpam-3759	155	1	then	then	ADV
ejpam-3759	155	2	there	there	PRON
ejpam-3759	155	3	exist	exist	VERB
ejpam-3759	155	4	α	α	PRON
ejpam-3759	155	5	,	,	PUNCT
ejpam-3759	155	6	β	β	X
ejpam-3759	155	7	∈	∈	PROPN
ejpam-3759	155	8	γ	γ	NOUN
ejpam-3759	155	9	such	such	ADJ
ejpam-3759	155	10	that	that	SCONJ
ejpam-3759	155	11	(	(	PUNCT
ejpam-3759	155	12	χb	χb	ADP
ejpam-3759	155	13	◦	◦	NOUN
ejpam-3759	155	14	αmt	αmt	NOUN
ejpam-3759	155	15	◦	◦	NOUN
ejpam-3759	155	16	β	β	X
ejpam-3759	155	17	χb	χb	NOUN
ejpam-3759	155	18	)	)	PUNCT
ejpam-3759	155	19	∩	∩	NOUN
ejpam-3759	155	20	χb	χb	ADP
ejpam-3759	155	21	6=	6=	PROPN
ejpam-3759	155	22	0	0	NUM
ejpam-3759	155	23	,	,	PUNCT
ejpam-3759	155	24	so	so	SCONJ
ejpam-3759	155	25	[	[	X
ejpam-3759	155	26	(	(	PUNCT
ejpam-3759	155	27	χb	χb	ADP
ejpam-3759	155	28	◦	◦	NOUN
ejpam-3759	155	29	αmt	αmt	NOUN
ejpam-3759	155	30	◦	◦	NOUN
ejpam-3759	155	31	β	β	X
ejpam-3759	155	32	χb	χb	NOUN
ejpam-3759	155	33	)	)	PUNCT
ejpam-3759	155	34	∩	∩	NOUN
ejpam-3759	155	35	χb](y	χb](y	NUM
ejpam-3759	155	36	)	)	PUNCT
ejpam-3759	155	37	6=	6=	ADP
ejpam-3759	155	38	0	0	NUM
ejpam-3759	155	39	for	for	ADP
ejpam-3759	155	40	some	some	DET
ejpam-3759	155	41	y	y	PROPN
ejpam-3759	155	42	∈	∈	PROPN
ejpam-3759	155	43	m.	m.	NOUN
ejpam-3759	155	44	hence	hence	ADV
ejpam-3759	155	45	,	,	PUNCT
ejpam-3759	155	46	y	y	PROPN
ejpam-3759	155	47	∈	∈	PROPN
ejpam-3759	155	48	b	b	PROPN
ejpam-3759	155	49	and	and	CCONJ
ejpam-3759	155	50	y	y	PROPN
ejpam-3759	155	51	=	=	NOUN
ejpam-3759	155	52	aαmβb	aαmβb	PROPN
ejpam-3759	155	53	for	for	ADP
ejpam-3759	155	54	some	some	DET
ejpam-3759	155	55	a	a	PRON
ejpam-3759	155	56	,	,	PUNCT
ejpam-3759	155	57	b	b	PROPN
ejpam-3759	155	58	∈	∈	PROPN
ejpam-3759	155	59	b	b	PROPN
ejpam-3759	155	60	and	and	CCONJ
ejpam-3759	155	61	α	α	NOUN
ejpam-3759	155	62	,	,	PUNCT
ejpam-3759	155	63	β	β	PROPN
ejpam-3759	155	64	∈	∈	PROPN
ejpam-3759	155	65	γ	γ	X
ejpam-3759	155	66	.	.	PROPN
ejpam-3759	155	67	therefore	therefore	ADV
ejpam-3759	155	68	,	,	PUNCT
ejpam-3759	155	69	y	y	PROPN
ejpam-3759	155	70	∈	∈	PROPN
ejpam-3759	155	71	bγmγb∩b	bγmγb∩b	PROPN
ejpam-3759	155	72	.	.	PUNCT
ejpam-3759	156	1	so	so	ADV
ejpam-3759	156	2	bγmγb∩b	bγmγb∩b	PUNCT
ejpam-3759	156	3	6=	6=	ADP
ejpam-3759	156	4	∅.	∅.	VERB
ejpam-3759	156	5	consequently	consequently	ADV
ejpam-3759	156	6	,	,	PUNCT
ejpam-3759	156	7	b	b	PROPN
ejpam-3759	156	8	is	be	AUX
ejpam-3759	156	9	an	an	DET
ejpam-3759	156	10	almost	almost	ADV
ejpam-3759	156	11	bi	bi	ADJ
ejpam-3759	156	12	-	-	ADJ
ejpam-3759	156	13	γ	γ	NOUN
ejpam-3759	156	14	-	-	NOUN
ejpam-3759	156	15	ideal	ideal	NOUN
ejpam-3759	156	16	of	of	ADP
ejpam-3759	156	17	m	m	PROPN
ejpam-3759	156	18	theorem	theorem	VERB
ejpam-3759	156	19	6	6	NUM
ejpam-3759	156	20	.	.	PUNCT
ejpam-3759	157	1	a	a	DET
ejpam-3759	157	2	fuzzy	fuzzy	ADJ
ejpam-3759	157	3	subset	subset	NOUN
ejpam-3759	157	4	f	f	PROPN
ejpam-3759	157	5	of	of	ADP
ejpam-3759	157	6	a	a	DET
ejpam-3759	157	7	γ	γ	PROPN
ejpam-3759	157	8	-	-	PUNCT
ejpam-3759	157	9	semigroup	semigroup	NOUN
ejpam-3759	157	10	m	m	VERB
ejpam-3759	157	11	is	be	AUX
ejpam-3759	157	12	a	a	DET
ejpam-3759	157	13	fuzzy	fuzzy	ADJ
ejpam-3759	157	14	almost	almost	ADV
ejpam-3759	157	15	bi	bi	ADJ
ejpam-3759	157	16	-	-	ADJ
ejpam-3759	157	17	γ	γ	NOUN
ejpam-3759	157	18	-	-	NOUN
ejpam-3759	157	19	ideal	ideal	NOUN
ejpam-3759	157	20	of	of	ADP
ejpam-3759	157	21	m	m	PRON
ejpam-3759	157	22	if	if	SCONJ
ejpam-3759	158	1	and	and	CCONJ
ejpam-3759	158	2	only	only	ADV
ejpam-3759	158	3	if	if	SCONJ
ejpam-3759	158	4	supp(f	supp(f	PROPN
ejpam-3759	158	5	)	)	PUNCT
ejpam-3759	158	6	is	be	AUX
ejpam-3759	158	7	an	an	DET
ejpam-3759	158	8	almost	almost	ADV
ejpam-3759	158	9	bi	bi	ADJ
ejpam-3759	158	10	-	-	ADJ
ejpam-3759	158	11	γ	γ	NOUN
ejpam-3759	158	12	-	-	NOUN
ejpam-3759	158	13	ideal	ideal	NOUN
ejpam-3759	158	14	of	of	ADP
ejpam-3759	158	15	m	m	PROPN
ejpam-3759	158	16	.	.	PUNCT
ejpam-3759	159	1	proof	proof	NOUN
ejpam-3759	159	2	.	.	PUNCT
ejpam-3759	160	1	assume	assume	VERB
ejpam-3759	160	2	that	that	SCONJ
ejpam-3759	160	3	f	f	PROPN
ejpam-3759	160	4	is	be	AUX
ejpam-3759	160	5	a	a	DET
ejpam-3759	160	6	fuzzy	fuzzy	ADJ
ejpam-3759	160	7	almost	almost	ADV
ejpam-3759	160	8	bi	bi	ADJ
ejpam-3759	160	9	-	-	ADJ
ejpam-3759	160	10	γ	γ	NOUN
ejpam-3759	160	11	-	-	NOUN
ejpam-3759	160	12	ideal	ideal	NOUN
ejpam-3759	160	13	of	of	ADP
ejpam-3759	160	14	a	a	DET
ejpam-3759	160	15	γ	γ	NOUN
ejpam-3759	160	16	-	-	PUNCT
ejpam-3759	160	17	semigroup	semigroup	NOUN
ejpam-3759	160	18	m	m	NOUN
ejpam-3759	160	19	and	and	CCONJ
ejpam-3759	160	20	let	let	VERB
ejpam-3759	160	21	m	m	PRON
ejpam-3759	160	22	∈m	∈m	ADJ
ejpam-3759	160	23	and	and	CCONJ
ejpam-3759	160	24	t	t	NOUN
ejpam-3759	160	25	∈	∈	PROPN
ejpam-3759	160	26	(	(	PUNCT
ejpam-3759	160	27	0	0	NUM
ejpam-3759	160	28	,	,	PUNCT
ejpam-3759	160	29	1	1	NUM
ejpam-3759	160	30	]	]	PUNCT
ejpam-3759	160	31	.	.	PUNCT
ejpam-3759	161	1	then	then	ADV
ejpam-3759	161	2	there	there	PRON
ejpam-3759	161	3	exist	exist	VERB
ejpam-3759	161	4	α	α	PRON
ejpam-3759	161	5	,	,	PUNCT
ejpam-3759	161	6	β	β	X
ejpam-3759	161	7	∈	∈	PROPN
ejpam-3759	161	8	γ	γ	NOUN
ejpam-3759	161	9	such	such	ADJ
ejpam-3759	161	10	that	that	PRON
ejpam-3759	161	11	(	(	PUNCT
ejpam-3759	161	12	f	f	PROPN
ejpam-3759	161	13	◦	◦	NOUN
ejpam-3759	161	14	αmt	αmt	NOUN
ejpam-3759	161	15	◦	◦	NOUN
ejpam-3759	161	16	β	β	NOUN
ejpam-3759	161	17	f)∩f	f)∩f	NOUN
ejpam-3759	161	18	6=	6=	ADP
ejpam-3759	161	19	0	0	NUM
ejpam-3759	161	20	.	.	PUNCT
ejpam-3759	162	1	hence	hence	ADV
ejpam-3759	162	2	,	,	PUNCT
ejpam-3759	162	3	[	[	X
ejpam-3759	162	4	(	(	PUNCT
ejpam-3759	162	5	f	f	PROPN
ejpam-3759	162	6	◦	◦	NOUN
ejpam-3759	162	7	αmt	αmt	NOUN
ejpam-3759	162	8	◦	◦	NOUN
ejpam-3759	162	9	β	β	NOUN
ejpam-3759	162	10	f	f	NOUN
ejpam-3759	162	11	)	)	PUNCT
ejpam-3759	162	12	∩	∩	PROPN
ejpam-3759	162	13	f	f	X
ejpam-3759	162	14	]	]	X
ejpam-3759	162	15	(	(	PUNCT
ejpam-3759	162	16	x	x	X
ejpam-3759	162	17	)	)	PUNCT
ejpam-3759	162	18	6=	6=	ADP
ejpam-3759	162	19	0	0	NUM
ejpam-3759	162	20	for	for	ADP
ejpam-3759	162	21	some	some	DET
ejpam-3759	162	22	x	x	SYM
ejpam-3759	162	23	∈	∈	PROPN
ejpam-3759	162	24	m	m	NOUN
ejpam-3759	162	25	.	.	PUNCT
ejpam-3759	163	1	so	so	ADV
ejpam-3759	163	2	there	there	PRON
ejpam-3759	163	3	exist	exist	VERB
ejpam-3759	163	4	y1	y1	NOUN
ejpam-3759	163	5	,	,	PUNCT
ejpam-3759	163	6	y2	y2	PROPN
ejpam-3759	163	7	∈	∈	PROPN
ejpam-3759	163	8	s	s	VERB
ejpam-3759	163	9	such	such	ADJ
ejpam-3759	163	10	that	that	SCONJ
ejpam-3759	163	11	x	x	PROPN
ejpam-3759	163	12	=	=	SYM
ejpam-3759	163	13	y1αmβy2	y1αmβy2	PROPN
ejpam-3759	163	14	,	,	PUNCT
ejpam-3759	163	15	f(x	f(x	PROPN
ejpam-3759	163	16	)	)	PUNCT
ejpam-3759	163	17	6=	6=	ADP
ejpam-3759	163	18	0	0	NUM
ejpam-3759	163	19	,	,	PUNCT
ejpam-3759	163	20	f(y1	f(y1	NOUN
ejpam-3759	163	21	)	)	PUNCT
ejpam-3759	163	22	6=	6=	ADP
ejpam-3759	163	23	0	0	NUM
ejpam-3759	163	24	and	and	CCONJ
ejpam-3759	163	25	f(y2	f(y2	ADJ
ejpam-3759	163	26	)	)	PUNCT
ejpam-3759	163	27	6=	6=	ADP
ejpam-3759	163	28	0	0	X
ejpam-3759	163	29	.	.	PUNCT
ejpam-3759	164	1	that	that	PRON
ejpam-3759	164	2	is	be	AUX
ejpam-3759	164	3	x	x	X
ejpam-3759	164	4	,	,	PUNCT
ejpam-3759	164	5	y1	y1	INTJ
ejpam-3759	164	6	,	,	PUNCT
ejpam-3759	164	7	y2	y2	PROPN
ejpam-3759	164	8	∈	∈	PROPN
ejpam-3759	164	9	supp(f	supp(f	PROPN
ejpam-3759	164	10	)	)	PUNCT
ejpam-3759	164	11	.	.	PUNCT
ejpam-3759	165	1	thus	thus	ADV
ejpam-3759	165	2	[	[	X
ejpam-3759	165	3	χsupp(f)	χsupp(f)	ADP
ejpam-3759	165	4	◦	◦	NOUN
ejpam-3759	165	5	αst	αst	NOUN
ejpam-3759	165	6	◦	◦	NOUN
ejpam-3759	165	7	βχsupp(f)](x	βχsupp(f)](x	PUNCT
ejpam-3759	165	8	)	)	PUNCT
ejpam-3759	165	9	6=	6=	ADP
ejpam-3759	165	10	0	0	NUM
ejpam-3759	165	11	and	and	CCONJ
ejpam-3759	165	12	χsupp(f)(x	χsupp(f)(x	PROPN
ejpam-3759	165	13	)	)	PUNCT
ejpam-3759	165	14	6=	6=	ADP
ejpam-3759	165	15	0	0	X
ejpam-3759	165	16	.	.	PUNCT
ejpam-3759	166	1	therefore	therefore	ADV
ejpam-3759	166	2	,	,	PUNCT
ejpam-3759	166	3	(	(	PUNCT
ejpam-3759	166	4	χsupp(f	χsupp(f	NOUN
ejpam-3759	166	5	)	)	PUNCT
ejpam-3759	166	6	◦	◦	NOUN
ejpam-3759	166	7	αmt	αmt	NOUN
ejpam-3759	166	8	◦	◦	NOUN
ejpam-3759	166	9	β	β	X
ejpam-3759	166	10	χsupp(f))∩χsupp(f	χsupp(f))∩χsupp(f	PROPN
ejpam-3759	166	11	)	)	PUNCT
ejpam-3759	166	12	6=	6=	ADP
ejpam-3759	166	13	0	0	X
ejpam-3759	166	14	.	.	PUNCT
ejpam-3759	167	1	hence	hence	ADV
ejpam-3759	167	2	,	,	PUNCT
ejpam-3759	167	3	χsupp(f	χsupp(f	PROPN
ejpam-3759	167	4	)	)	PUNCT
ejpam-3759	167	5	is	be	AUX
ejpam-3759	167	6	a	a	DET
ejpam-3759	167	7	fuzzy	fuzzy	ADJ
ejpam-3759	167	8	almost	almost	ADV
ejpam-3759	167	9	bi	bi	ADJ
ejpam-3759	167	10	-	-	ADJ
ejpam-3759	167	11	γ	γ	NOUN
ejpam-3759	167	12	-	-	NOUN
ejpam-3759	167	13	ideal	ideal	NOUN
ejpam-3759	167	14	of	of	ADP
ejpam-3759	167	15	m.	m.	NOUN
ejpam-3759	167	16	by	by	ADP
ejpam-3759	167	17	theorem	theorem	NOUN
ejpam-3759	167	18	5	5	NUM
ejpam-3759	167	19	,	,	PUNCT
ejpam-3759	167	20	supp(f	supp(f	PROPN
ejpam-3759	167	21	)	)	PUNCT
ejpam-3759	167	22	is	be	AUX
ejpam-3759	167	23	an	an	DET
ejpam-3759	167	24	almost	almost	ADV
ejpam-3759	167	25	bi	bi	ADJ
ejpam-3759	167	26	-	-	ADJ
ejpam-3759	167	27	γ	γ	NOUN
ejpam-3759	167	28	-	-	NOUN
ejpam-3759	167	29	ideal	ideal	NOUN
ejpam-3759	167	30	of	of	ADP
ejpam-3759	167	31	m.	m.	NOUN
ejpam-3759	167	32	on	on	ADP
ejpam-3759	167	33	the	the	DET
ejpam-3759	167	34	other	other	ADJ
ejpam-3759	167	35	hand	hand	NOUN
ejpam-3759	167	36	,	,	PUNCT
ejpam-3759	167	37	we	we	PRON
ejpam-3759	167	38	assume	assume	VERB
ejpam-3759	167	39	that	that	SCONJ
ejpam-3759	167	40	supp(f	supp(f	PROPN
ejpam-3759	167	41	)	)	PUNCT
ejpam-3759	167	42	is	be	AUX
ejpam-3759	167	43	an	an	DET
ejpam-3759	167	44	almost	almost	ADV
ejpam-3759	167	45	bi	bi	ADJ
ejpam-3759	167	46	-	-	ADJ
ejpam-3759	167	47	γ	γ	NOUN
ejpam-3759	167	48	-	-	NOUN
ejpam-3759	167	49	ideal	ideal	NOUN
ejpam-3759	167	50	of	of	ADP
ejpam-3759	167	51	m.	m.	NOUN
ejpam-3759	167	52	it	it	PRON
ejpam-3759	167	53	follows	follow	VERB
ejpam-3759	167	54	from	from	ADP
ejpam-3759	167	55	theorem	theorem	ADJ
ejpam-3759	167	56	5	5	NUM
ejpam-3759	167	57	that	that	PRON
ejpam-3759	167	58	χsupp(f	χsupp(f	PROPN
ejpam-3759	167	59	)	)	PUNCT
ejpam-3759	167	60	is	be	AUX
ejpam-3759	167	61	a	a	DET
ejpam-3759	167	62	fuzzy	fuzzy	ADJ
ejpam-3759	167	63	almost	almost	ADV
ejpam-3759	167	64	bi	bi	ADJ
ejpam-3759	167	65	-	-	ADJ
ejpam-3759	167	66	γ	γ	NOUN
ejpam-3759	167	67	-	-	NOUN
ejpam-3759	167	68	ideal	ideal	NOUN
ejpam-3759	167	69	of	of	ADP
ejpam-3759	167	70	m.	m.	NOUN
ejpam-3759	167	71	let	let	VERB
ejpam-3759	167	72	mt	mt	PROPN
ejpam-3759	167	73	be	be	AUX
ejpam-3759	167	74	any	any	DET
ejpam-3759	167	75	fuzzy	fuzzy	ADJ
ejpam-3759	167	76	point	point	NOUN
ejpam-3759	167	77	of	of	ADP
ejpam-3759	167	78	m.	m.	NOUN
ejpam-3759	167	79	thus	thus	ADV
ejpam-3759	167	80	,	,	PUNCT
ejpam-3759	167	81	(	(	PUNCT
ejpam-3759	167	82	χsupp(f	χsupp(f	NOUN
ejpam-3759	167	83	)	)	PUNCT
ejpam-3759	167	84	◦	◦	NOUN
ejpam-3759	167	85	αmt	αmt	NOUN
ejpam-3759	167	86	◦	◦	NOUN
ejpam-3759	167	87	β	β	X
ejpam-3759	167	88	χsupp(f))∩χsupp(f	χsupp(f))∩χsupp(f	PROPN
ejpam-3759	167	89	)	)	PUNCT
ejpam-3759	167	90	6=	6=	ADP
ejpam-3759	167	91	0	0	NUM
ejpam-3759	167	92	for	for	ADP
ejpam-3759	167	93	some	some	DET
ejpam-3759	167	94	α	α	NOUN
ejpam-3759	167	95	,	,	PUNCT
ejpam-3759	167	96	β	β	PROPN
ejpam-3759	167	97	∈	∈	PROPN
ejpam-3759	167	98	γ	γ	X
ejpam-3759	167	99	.	.	PUNCT
ejpam-3759	168	1	then	then	ADV
ejpam-3759	168	2	there	there	PRON
ejpam-3759	168	3	exists	exist	VERB
ejpam-3759	168	4	an	an	DET
ejpam-3759	168	5	element	element	NOUN
ejpam-3759	168	6	x	x	PUNCT
ejpam-3759	168	7	in	in	ADP
ejpam-3759	168	8	m	m	PRON
ejpam-3759	168	9	such	such	ADJ
ejpam-3759	168	10	that	that	SCONJ
ejpam-3759	168	11	[	[	X
ejpam-3759	168	12	(	(	PUNCT
ejpam-3759	168	13	χsupp(f	χsupp(f	NOUN
ejpam-3759	168	14	)	)	PUNCT
ejpam-3759	168	15	◦	◦	NOUN
ejpam-3759	168	16	α	α	PROPN
ejpam-3759	168	17	mt	mt	PROPN
ejpam-3759	168	18	◦	◦	PROPN
ejpam-3759	168	19	β	β	PROPN
ejpam-3759	168	20	χsupp(f	χsupp(f	PROPN
ejpam-3759	168	21	)	)	PUNCT
ejpam-3759	168	22	)	)	PUNCT
ejpam-3759	168	23	∩	∩	NOUN
ejpam-3759	168	24	χsupp(f)](x	χsupp(f)](x	NOUN
ejpam-3759	168	25	)	)	PUNCT
ejpam-3759	168	26	6=	6=	ADP
ejpam-3759	168	27	0	0	X
ejpam-3759	168	28	.	.	PUNCT
ejpam-3759	169	1	therefore	therefore	ADV
ejpam-3759	169	2	,	,	PUNCT
ejpam-3759	169	3	(	(	PUNCT
ejpam-3759	169	4	χsupp(f)	χsupp(f)	NOUN
ejpam-3759	169	5	◦	◦	NOUN
ejpam-3759	169	6	αmt	αmt	NOUN
ejpam-3759	169	7	◦	◦	NOUN
ejpam-3759	169	8	βχsupp(f))(x	βχsupp(f))(x	NOUN
ejpam-3759	169	9	)	)	PUNCT
ejpam-3759	170	1	6=	6=	ADP
ejpam-3759	170	2	0	0	NUM
ejpam-3759	170	3	and	and	CCONJ
ejpam-3759	170	4	χsupp(f)(x	χsupp(f)(x	PROPN
ejpam-3759	170	5	)	)	PUNCT
ejpam-3759	170	6	6=	6=	ADP
ejpam-3759	170	7	0	0	X
ejpam-3759	170	8	.	.	PUNCT
ejpam-3759	171	1	then	then	ADV
ejpam-3759	171	2	there	there	PRON
ejpam-3759	171	3	exist	exist	VERB
ejpam-3759	171	4	y1	y1	NOUN
ejpam-3759	171	5	,	,	PUNCT
ejpam-3759	171	6	y2	y2	PROPN
ejpam-3759	171	7	∈m	∈m	NOUN
ejpam-3759	171	8	such	such	ADJ
ejpam-3759	171	9	that	that	SCONJ
ejpam-3759	171	10	x	x	PROPN
ejpam-3759	171	11	=	=	SYM
ejpam-3759	171	12	y1αmβy2	y1αmβy2	PROPN
ejpam-3759	171	13	,	,	PUNCT
ejpam-3759	171	14	f(x	f(x	PROPN
ejpam-3759	171	15	)	)	PUNCT
ejpam-3759	171	16	6=	6=	ADP
ejpam-3759	171	17	0	0	NUM
ejpam-3759	171	18	,	,	PUNCT
ejpam-3759	171	19	f(y1	f(y1	NOUN
ejpam-3759	171	20	)	)	PUNCT
ejpam-3759	171	21	6=	6=	ADP
ejpam-3759	171	22	0	0	NUM
ejpam-3759	171	23	and	and	CCONJ
ejpam-3759	171	24	f(y2	f(y2	ADJ
ejpam-3759	171	25	)	)	PUNCT
ejpam-3759	171	26	6=	6=	ADP
ejpam-3759	171	27	0	0	X
ejpam-3759	171	28	.	.	PUNCT
ejpam-3759	172	1	this	this	PRON
ejpam-3759	172	2	means	mean	VERB
ejpam-3759	172	3	that	that	SCONJ
ejpam-3759	172	4	(	(	PUNCT
ejpam-3759	172	5	f	f	X
ejpam-3759	172	6	◦	◦	NOUN
ejpam-3759	172	7	αmt	αmt	NOUN
ejpam-3759	172	8	◦	◦	NOUN
ejpam-3759	172	9	β	β	NOUN
ejpam-3759	172	10	f	f	NOUN
ejpam-3759	172	11	)	)	PUNCT
ejpam-3759	172	12	∩	∩	PROPN
ejpam-3759	172	13	f	f	PROPN
ejpam-3759	172	14	6=	6=	PROPN
ejpam-3759	172	15	0	0	NUM
ejpam-3759	172	16	.	.	PUNCT
ejpam-3759	173	1	we	we	PRON
ejpam-3759	173	2	conclude	conclude	VERB
ejpam-3759	173	3	that	that	SCONJ
ejpam-3759	173	4	f	f	PROPN
ejpam-3759	173	5	is	be	AUX
ejpam-3759	173	6	a	a	DET
ejpam-3759	173	7	fuzzy	fuzzy	ADJ
ejpam-3759	173	8	almost	almost	ADV
ejpam-3759	173	9	bi	bi	ADJ
ejpam-3759	173	10	-	-	ADJ
ejpam-3759	173	11	γ	γ	NOUN
ejpam-3759	173	12	-	-	NOUN
ejpam-3759	173	13	ideal	ideal	NOUN
ejpam-3759	173	14	of	of	ADP
ejpam-3759	173	15	m.	m.	NOUN
ejpam-3759	173	16	next	next	ADV
ejpam-3759	173	17	,	,	PUNCT
ejpam-3759	173	18	we	we	PRON
ejpam-3759	173	19	will	will	AUX
ejpam-3759	173	20	study	study	VERB
ejpam-3759	173	21	the	the	DET
ejpam-3759	173	22	minimality	minimality	NOUN
ejpam-3759	173	23	of	of	ADP
ejpam-3759	173	24	fuzzy	fuzzy	ADJ
ejpam-3759	173	25	almost	almost	ADV
ejpam-3759	173	26	bi	bi	ADJ
ejpam-3759	173	27	-	-	ADJ
ejpam-3759	173	28	γ	γ	NOUN
ejpam-3759	173	29	-	-	PUNCT
ejpam-3759	173	30	ideals	ideal	NOUN
ejpam-3759	173	31	.	.	PUNCT
ejpam-3759	174	1	definition	definition	NOUN
ejpam-3759	174	2	5	5	NUM
ejpam-3759	174	3	.	.	PUNCT
ejpam-3759	175	1	a	a	DET
ejpam-3759	175	2	fuzzy	fuzzy	ADJ
ejpam-3759	175	3	almost	almost	ADV
ejpam-3759	175	4	bi	bi	ADJ
ejpam-3759	175	5	-	-	ADJ
ejpam-3759	175	6	γ	γ	ADJ
ejpam-3759	175	7	-	-	PUNCT
ejpam-3759	175	8	ideal	ideal	ADJ
ejpam-3759	175	9	f	f	NOUN
ejpam-3759	175	10	of	of	ADP
ejpam-3759	175	11	a	a	DET
ejpam-3759	175	12	γ	γ	PROPN
ejpam-3759	175	13	-	-	PUNCT
ejpam-3759	175	14	semigroup	semigroup	NOUN
ejpam-3759	175	15	m	m	VERB
ejpam-3759	175	16	is	be	AUX
ejpam-3759	175	17	called	call	VERB
ejpam-3759	175	18	minimal	minimal	ADJ
ejpam-3759	175	19	if	if	SCONJ
ejpam-3759	175	20	for	for	ADP
ejpam-3759	175	21	all	all	PRON
ejpam-3759	175	22	fuzzy	fuzzy	ADJ
ejpam-3759	175	23	almost	almost	ADV
ejpam-3759	175	24	bi	bi	ADJ
ejpam-3759	175	25	-	-	ADJ
ejpam-3759	175	26	γ	γ	NOUN
ejpam-3759	175	27	-	-	PUNCT
ejpam-3759	175	28	ideal	ideal	ADJ
ejpam-3759	175	29	g	g	NOUN
ejpam-3759	175	30	of	of	ADP
ejpam-3759	175	31	m	m	AUX
ejpam-3759	175	32	contained	contain	VERB
ejpam-3759	175	33	in	in	ADP
ejpam-3759	175	34	f	f	PROPN
ejpam-3759	175	35	,	,	PUNCT
ejpam-3759	175	36	we	we	PRON
ejpam-3759	175	37	must	must	AUX
ejpam-3759	175	38	have	have	VERB
ejpam-3759	175	39	supp(g	supp(g	NUM
ejpam-3759	175	40	)	)	PUNCT
ejpam-3759	175	41	=	=	SYM
ejpam-3759	175	42	supp(f	supp(f	PROPN
ejpam-3759	175	43	)	)	PUNCT
ejpam-3759	175	44	.	.	PUNCT
ejpam-3759	176	1	now	now	ADV
ejpam-3759	176	2	,	,	PUNCT
ejpam-3759	176	3	we	we	PRON
ejpam-3759	176	4	provide	provide	VERB
ejpam-3759	176	5	the	the	DET
ejpam-3759	176	6	relationship	relationship	NOUN
ejpam-3759	176	7	between	between	ADP
ejpam-3759	176	8	minimal	minimal	ADJ
ejpam-3759	176	9	almost	almost	ADV
ejpam-3759	176	10	bi	bi	ADJ
ejpam-3759	176	11	-	-	ADJ
ejpam-3759	176	12	γ	γ	NOUN
ejpam-3759	176	13	-	-	PUNCT
ejpam-3759	176	14	ideals	ideal	NOUN
ejpam-3759	176	15	and	and	CCONJ
ejpam-3759	176	16	their	their	PRON
ejpam-3759	176	17	fuzzification	fuzzification	NOUN
ejpam-3759	176	18	.	.	PUNCT
ejpam-3759	177	1	theorem	theorem	VERB
ejpam-3759	177	2	7	7	NUM
ejpam-3759	177	3	.	.	PUNCT
ejpam-3759	177	4	a	a	DET
ejpam-3759	177	5	non	non	ADJ
ejpam-3759	177	6	-	-	ADJ
ejpam-3759	177	7	empty	empty	ADJ
ejpam-3759	177	8	subset	subset	NOUN
ejpam-3759	177	9	a	a	PRON
ejpam-3759	177	10	of	of	ADP
ejpam-3759	177	11	a	a	DET
ejpam-3759	177	12	γ	γ	NOUN
ejpam-3759	177	13	-	-	PUNCT
ejpam-3759	177	14	semigroup	semigroup	NOUN
ejpam-3759	177	15	m	m	VERB
ejpam-3759	177	16	is	be	AUX
ejpam-3759	177	17	a	a	DET
ejpam-3759	177	18	minimal	minimal	ADJ
ejpam-3759	177	19	almost	almost	ADV
ejpam-3759	177	20	bi	bi	ADJ
ejpam-3759	177	21	-	-	ADJ
ejpam-3759	177	22	γ	γ	NOUN
ejpam-3759	177	23	-	-	NOUN
ejpam-3759	177	24	ideal	ideal	NOUN
ejpam-3759	177	25	of	of	ADP
ejpam-3759	177	26	m	m	PRON
ejpam-3759	177	27	if	if	SCONJ
ejpam-3759	178	1	and	and	CCONJ
ejpam-3759	178	2	only	only	ADV
ejpam-3759	178	3	if	if	SCONJ
ejpam-3759	178	4	χa	χa	PROPN
ejpam-3759	178	5	is	be	AUX
ejpam-3759	178	6	a	a	DET
ejpam-3759	178	7	minimal	minimal	ADJ
ejpam-3759	178	8	fuzzy	fuzzy	ADJ
ejpam-3759	178	9	almost	almost	ADV
ejpam-3759	178	10	bi	bi	ADJ
ejpam-3759	178	11	-	-	ADJ
ejpam-3759	178	12	γ	γ	NOUN
ejpam-3759	178	13	-	-	NOUN
ejpam-3759	178	14	ideal	ideal	NOUN
ejpam-3759	178	15	of	of	ADP
ejpam-3759	178	16	m	m	PROPN
ejpam-3759	178	17	.	.	PUNCT
ejpam-3759	179	1	proof	proof	NOUN
ejpam-3759	179	2	.	.	PUNCT
ejpam-3759	180	1	let	let	VERB
ejpam-3759	180	2	a	a	PRON
ejpam-3759	180	3	be	be	AUX
ejpam-3759	180	4	a	a	DET
ejpam-3759	180	5	minimal	minimal	ADJ
ejpam-3759	180	6	almost	almost	ADV
ejpam-3759	180	7	bi	bi	ADJ
ejpam-3759	180	8	-	-	ADJ
ejpam-3759	180	9	γ	γ	NOUN
ejpam-3759	180	10	-	-	NOUN
ejpam-3759	180	11	ideal	ideal	NOUN
ejpam-3759	180	12	of	of	ADP
ejpam-3759	180	13	a	a	DET
ejpam-3759	180	14	γ	γ	NOUN
ejpam-3759	180	15	-	-	PUNCT
ejpam-3759	180	16	semigroup	semigroup	NOUN
ejpam-3759	180	17	m	m	NOUN
ejpam-3759	180	18	.	.	PUNCT
ejpam-3759	181	1	by	by	ADP
ejpam-3759	181	2	theorem	theorem	NOUN
ejpam-3759	181	3	5	5	NUM
ejpam-3759	181	4	,	,	PUNCT
ejpam-3759	181	5	we	we	PRON
ejpam-3759	181	6	have	have	VERB
ejpam-3759	181	7	that	that	PRON
ejpam-3759	181	8	χa	χa	PROPN
ejpam-3759	181	9	is	be	AUX
ejpam-3759	181	10	a	a	DET
ejpam-3759	181	11	fuzzy	fuzzy	ADJ
ejpam-3759	181	12	almost	almost	ADV
ejpam-3759	181	13	bi	bi	ADJ
ejpam-3759	181	14	-	-	ADJ
ejpam-3759	181	15	γ	γ	NOUN
ejpam-3759	181	16	-	-	NOUN
ejpam-3759	181	17	ideal	ideal	NOUN
ejpam-3759	181	18	of	of	ADP
ejpam-3759	181	19	m.	m.	NOUN
ejpam-3759	181	20	assume	assume	VERB
ejpam-3759	181	21	that	that	SCONJ
ejpam-3759	181	22	g	g	PROPN
ejpam-3759	181	23	is	be	AUX
ejpam-3759	181	24	a	a	DET
ejpam-3759	181	25	fuzzy	fuzzy	ADJ
ejpam-3759	181	26	almost	almost	ADV
ejpam-3759	181	27	bi	bi	ADJ
ejpam-3759	181	28	-	-	ADJ
ejpam-3759	181	29	γ	γ	NOUN
ejpam-3759	181	30	-	-	NOUN
ejpam-3759	181	31	ideal	ideal	NOUN
ejpam-3759	181	32	of	of	ADP
ejpam-3759	181	33	m	m	AUX
ejpam-3759	181	34	contained	contain	VERB
ejpam-3759	181	35	in	in	ADP
ejpam-3759	181	36	χa	χa	PROPN
ejpam-3759	181	37	.	.	PUNCT
ejpam-3759	182	1	thus	thus	ADV
ejpam-3759	182	2	,	,	PUNCT
ejpam-3759	182	3	supp(g	supp(g	NUM
ejpam-3759	182	4	)	)	PUNCT
ejpam-3759	182	5	⊆	⊆	NUM
ejpam-3759	182	6	supp(χa	supp(χa	NOUN
ejpam-3759	182	7	)	)	PUNCT
ejpam-3759	182	8	=	=	PUNCT
ejpam-3759	183	1	a.	a.	NOUN
ejpam-3759	183	2	because	because	SCONJ
ejpam-3759	183	3	of	of	ADP
ejpam-3759	183	4	g	g	PROPN
ejpam-3759	183	5	⊆	⊆	NUM
ejpam-3759	183	6	χsupp(g	χsupp(g	NOUN
ejpam-3759	183	7	)	)	PUNCT
ejpam-3759	183	8	,	,	PUNCT
ejpam-3759	183	9	we	we	PRON
ejpam-3759	183	10	have	have	VERB
ejpam-3759	183	11	(	(	PUNCT
ejpam-3759	183	12	g	g	NOUN
ejpam-3759	183	13	◦	◦	NOUN
ejpam-3759	183	14	αmt	αmt	NOUN
ejpam-3759	183	15	◦	◦	NOUN
ejpam-3759	183	16	β	β	X
ejpam-3759	183	17	g)∩g	g)∩g	NOUN
ejpam-3759	183	18	⊆	⊆	NUM
ejpam-3759	183	19	(	(	PUNCT
ejpam-3759	183	20	χsupp(g	χsupp(g	NOUN
ejpam-3759	183	21	)	)	PUNCT
ejpam-3759	183	22	◦	◦	NOUN
ejpam-3759	183	23	αmt	αmt	NOUN
ejpam-3759	183	24	◦	◦	NOUN
ejpam-3759	183	25	β	β	X
ejpam-3759	183	26	χsupp(g))∩χsupp(g	χsupp(g))∩χsupp(g	PROPN
ejpam-3759	183	27	)	)	PUNCT
ejpam-3759	183	28	for	for	ADP
ejpam-3759	183	29	all	all	DET
ejpam-3759	183	30	fuzzy	fuzzy	ADJ
ejpam-3759	183	31	points	point	NOUN
ejpam-3759	183	32	mt	mt	PROPN
ejpam-3759	183	33	of	of	ADP
ejpam-3759	183	34	m	m	PROPN
ejpam-3759	183	35	.	.	PUNCT
ejpam-3759	184	1	thus	thus	ADV
ejpam-3759	184	2	χsupp(g	χsupp(g	NOUN
ejpam-3759	184	3	)	)	PUNCT
ejpam-3759	184	4	is	be	AUX
ejpam-3759	184	5	a	a	DET
ejpam-3759	184	6	fuzzy	fuzzy	ADJ
ejpam-3759	184	7	almost	almost	ADV
ejpam-3759	184	8	bi	bi	ADJ
ejpam-3759	184	9	-	-	ADJ
ejpam-3759	184	10	γ	γ	NOUN
ejpam-3759	184	11	-	-	NOUN
ejpam-3759	184	12	ideal	ideal	NOUN
ejpam-3759	184	13	of	of	ADP
ejpam-3759	184	14	m.	m.	NOUN
ejpam-3759	184	15	by	by	ADP
ejpam-3759	184	16	theorem	theorem	NOUN
ejpam-3759	184	17	5	5	NUM
ejpam-3759	184	18	,	,	PUNCT
ejpam-3759	184	19	supp(g	supp(g	NOUN
ejpam-3759	184	20	)	)	PUNCT
ejpam-3759	184	21	is	be	AUX
ejpam-3759	184	22	an	an	DET
ejpam-3759	184	23	almost	almost	ADV
ejpam-3759	184	24	bi	bi	ADJ
ejpam-3759	184	25	-	-	ADJ
ejpam-3759	184	26	γ	γ	NOUN
ejpam-3759	184	27	-	-	NOUN
ejpam-3759	184	28	ideal	ideal	NOUN
ejpam-3759	184	29	of	of	ADP
ejpam-3759	184	30	m.	m.	NOUN
ejpam-3759	184	31	because	because	SCONJ
ejpam-3759	184	32	of	of	ADP
ejpam-3759	184	33	a	a	PRON
ejpam-3759	184	34	is	be	AUX
ejpam-3759	184	35	a	a	DET
ejpam-3759	184	36	minimal	minimal	ADJ
ejpam-3759	184	37	,	,	PUNCT
ejpam-3759	184	38	then	then	ADV
ejpam-3759	184	39	supp(g	supp(g	NOUN
ejpam-3759	184	40	)	)	PUNCT
ejpam-3759	184	41	=	=	PUNCT
ejpam-3759	185	1	a	a	DET
ejpam-3759	185	2	=	=	SYM
ejpam-3759	185	3	supp(χa	supp(χa	NOUN
ejpam-3759	185	4	)	)	PUNCT
ejpam-3759	185	5	.	.	PUNCT
ejpam-3759	186	1	therefore	therefore	ADV
ejpam-3759	186	2	,	,	PUNCT
ejpam-3759	186	3	χa	χa	PROPN
ejpam-3759	186	4	is	be	AUX
ejpam-3759	186	5	minimal	minimal	ADJ
ejpam-3759	186	6	.	.	PUNCT
ejpam-3759	187	1	to	to	PART
ejpam-3759	187	2	prove	prove	VERB
ejpam-3759	187	3	the	the	DET
ejpam-3759	187	4	converse	converse	NOUN
ejpam-3759	187	5	,	,	PUNCT
ejpam-3759	187	6	assume	assume	VERB
ejpam-3759	187	7	that	that	SCONJ
ejpam-3759	187	8	χa	χa	PROPN
ejpam-3759	187	9	is	be	AUX
ejpam-3759	187	10	a	a	DET
ejpam-3759	187	11	minimal	minimal	ADJ
ejpam-3759	187	12	fuzzy	fuzzy	ADJ
ejpam-3759	187	13	almost	almost	ADV
ejpam-3759	187	14	bi	bi	ADJ
ejpam-3759	187	15	-	-	ADJ
ejpam-3759	187	16	γ	γ	NOUN
ejpam-3759	187	17	-	-	NOUN
ejpam-3759	187	18	ideal	ideal	NOUN
ejpam-3759	187	19	of	of	ADP
ejpam-3759	187	20	m	m	PROPN
ejpam-3759	187	21	and	and	CCONJ
ejpam-3759	187	22	b	b	PROPN
ejpam-3759	187	23	is	be	AUX
ejpam-3759	187	24	an	an	DET
ejpam-3759	187	25	almost	almost	ADV
ejpam-3759	187	26	bi	bi	ADJ
ejpam-3759	187	27	-	-	ADJ
ejpam-3759	187	28	γ	γ	NOUN
ejpam-3759	187	29	-	-	NOUN
ejpam-3759	187	30	ideal	ideal	NOUN
ejpam-3759	187	31	of	of	ADP
ejpam-3759	187	32	m	m	AUX
ejpam-3759	187	33	contained	contain	VERB
ejpam-3759	187	34	in	in	ADP
ejpam-3759	187	35	a.	a.	NOUN
ejpam-3759	187	36	then	then	ADV
ejpam-3759	187	37	χb	χb	PROPN
ejpam-3759	187	38	is	be	AUX
ejpam-3759	187	39	a	a	DET
ejpam-3759	187	40	fuzzy	fuzzy	ADJ
ejpam-3759	187	41	almost	almost	ADV
ejpam-3759	187	42	bi	bi	ADJ
ejpam-3759	187	43	-	-	ADJ
ejpam-3759	187	44	γ	γ	NOUN
ejpam-3759	187	45	-	-	NOUN
ejpam-3759	187	46	ideal	ideal	NOUN
ejpam-3759	187	47	of	of	ADP
ejpam-3759	187	48	m	m	PROPN
ejpam-3759	187	49	and	and	CCONJ
ejpam-3759	187	50	χb	χb	PRON
ejpam-3759	187	51	⊆	⊆	NUM
ejpam-3759	187	52	χa	χa	NOUN
ejpam-3759	187	53	.	.	PUNCT
ejpam-3759	188	1	thus	thus	ADV
ejpam-3759	188	2	,	,	PUNCT
ejpam-3759	188	3	b	b	X
ejpam-3759	188	4	=	=	SYM
ejpam-3759	188	5	supp(χb	supp(χb	PROPN
ejpam-3759	188	6	)	)	PUNCT
ejpam-3759	188	7	=	=	SYM
ejpam-3759	188	8	supp(χa	supp(χa	NOUN
ejpam-3759	188	9	)	)	PUNCT
ejpam-3759	188	10	=	=	PUNCT
ejpam-3759	189	1	a.	a.	NOUN
ejpam-3759	189	2	we	we	PRON
ejpam-3759	189	3	conclude	conclude	VERB
ejpam-3759	189	4	that	that	SCONJ
ejpam-3759	189	5	a	a	PRON
ejpam-3759	189	6	is	be	AUX
ejpam-3759	189	7	minimal	minimal	ADJ
ejpam-3759	189	8	.	.	PUNCT
ejpam-3759	190	1	r.	r.	PROPN
ejpam-3759	190	2	chinram	chinram	PROPN
ejpam-3759	190	3	et	et	PROPN
ejpam-3759	190	4	al	al	PROPN
ejpam-3759	190	5	.	.	PUNCT
ejpam-3759	190	6	/	/	SYM
ejpam-3759	190	7	eur	eur	PROPN
ejpam-3759	190	8	.	.	PUNCT
ejpam-3759	191	1	j.	j.	PROPN
ejpam-3759	191	2	pure	pure	PROPN
ejpam-3759	191	3	appl	appl	PROPN
ejpam-3759	191	4	.	.	PROPN
ejpam-3759	191	5	math	math	PROPN
ejpam-3759	191	6	,	,	PUNCT
ejpam-3759	191	7	13	13	NUM
ejpam-3759	191	8	(	(	PUNCT
ejpam-3759	191	9	3	3	NUM
ejpam-3759	191	10	)	)	PUNCT
ejpam-3759	191	11	(	(	PUNCT
ejpam-3759	191	12	2020	2020	NUM
ejpam-3759	191	13	)	)	PUNCT
ejpam-3759	191	14	,	,	PUNCT
ejpam-3759	191	15	620	620	NUM
ejpam-3759	191	16	-	-	SYM
ejpam-3759	191	17	630	630	NUM
ejpam-3759	191	18	627	627	NUM
ejpam-3759	191	19	corollary	corollary	NOUN
ejpam-3759	191	20	3	3	NUM
ejpam-3759	191	21	.	.	PUNCT
ejpam-3759	192	1	a	a	DET
ejpam-3759	192	2	γ	γ	PROPN
ejpam-3759	192	3	-	-	PUNCT
ejpam-3759	192	4	semigroup	semigroup	NOUN
ejpam-3759	192	5	m	m	AUX
ejpam-3759	192	6	has	have	VERB
ejpam-3759	192	7	no	no	DET
ejpam-3759	192	8	proper	proper	ADJ
ejpam-3759	192	9	almost	almost	ADV
ejpam-3759	192	10	bi	bi	ADJ
ejpam-3759	192	11	-	-	ADJ
ejpam-3759	192	12	γ	γ	NOUN
ejpam-3759	192	13	-	-	PUNCT
ejpam-3759	192	14	ideals	ideal	NOUN
ejpam-3759	192	15	if	if	SCONJ
ejpam-3759	192	16	and	and	CCONJ
ejpam-3759	192	17	only	only	ADV
ejpam-3759	192	18	if	if	SCONJ
ejpam-3759	192	19	for	for	ADP
ejpam-3759	192	20	all	all	PRON
ejpam-3759	192	21	fuzzy	fuzzy	ADJ
ejpam-3759	192	22	almost	almost	ADV
ejpam-3759	192	23	bi	bi	ADJ
ejpam-3759	192	24	-	-	ADJ
ejpam-3759	192	25	γ	γ	ADJ
ejpam-3759	192	26	-	-	PUNCT
ejpam-3759	192	27	ideal	ideal	ADJ
ejpam-3759	192	28	f	f	PROPN
ejpam-3759	192	29	of	of	ADP
ejpam-3759	192	30	m	m	PROPN
ejpam-3759	192	31	,	,	PUNCT
ejpam-3759	192	32	supp(f	supp(f	PROPN
ejpam-3759	192	33	)	)	PUNCT
ejpam-3759	192	34	=	=	SYM
ejpam-3759	192	35	m.	m.	NOUN
ejpam-3759	192	36	proof	proof	NOUN
ejpam-3759	192	37	.	.	PUNCT
ejpam-3759	193	1	assume	assume	VERB
ejpam-3759	193	2	that	that	SCONJ
ejpam-3759	193	3	m	m	PROPN
ejpam-3759	193	4	has	have	VERB
ejpam-3759	193	5	no	no	DET
ejpam-3759	193	6	proper	proper	ADJ
ejpam-3759	193	7	almost	almost	ADV
ejpam-3759	193	8	bi	bi	ADJ
ejpam-3759	193	9	-	-	ADJ
ejpam-3759	193	10	γ	γ	NOUN
ejpam-3759	193	11	-	-	PUNCT
ejpam-3759	193	12	ideals	ideal	NOUN
ejpam-3759	193	13	and	and	CCONJ
ejpam-3759	193	14	let	let	VERB
ejpam-3759	193	15	f	f	PRON
ejpam-3759	193	16	be	be	AUX
ejpam-3759	193	17	a	a	DET
ejpam-3759	193	18	fuzzy	fuzzy	ADJ
ejpam-3759	193	19	almost	almost	ADV
ejpam-3759	193	20	biγ	biγ	NOUN
ejpam-3759	193	21	-	-	PUNCT
ejpam-3759	193	22	ideal	ideal	NOUN
ejpam-3759	193	23	of	of	ADP
ejpam-3759	193	24	m	m	PRON
ejpam-3759	193	25	.	.	PUNCT
ejpam-3759	194	1	by	by	ADP
ejpam-3759	194	2	theorem	theorem	NOUN
ejpam-3759	194	3	6	6	NUM
ejpam-3759	194	4	,	,	PUNCT
ejpam-3759	194	5	we	we	PRON
ejpam-3759	194	6	have	have	VERB
ejpam-3759	194	7	supp(f	supp(f	PROPN
ejpam-3759	194	8	)	)	PUNCT
ejpam-3759	195	1	is	be	AUX
ejpam-3759	195	2	almost	almost	ADV
ejpam-3759	195	3	bi	bi	ADJ
ejpam-3759	195	4	-	-	ADJ
ejpam-3759	195	5	γ	γ	NOUN
ejpam-3759	195	6	-	-	NOUN
ejpam-3759	195	7	ideal	ideal	NOUN
ejpam-3759	195	8	of	of	ADP
ejpam-3759	195	9	m	m	PROPN
ejpam-3759	195	10	.	.	PUNCT
ejpam-3759	196	1	thus	thus	ADV
ejpam-3759	196	2	supp(f	supp(f	NUM
ejpam-3759	196	3	)	)	PUNCT
ejpam-3759	196	4	=	=	NOUN
ejpam-3759	197	1	m	m	PROPN
ejpam-3759	197	2	.	.	PUNCT
ejpam-3759	198	1	to	to	PART
ejpam-3759	198	2	prove	prove	VERB
ejpam-3759	198	3	the	the	DET
ejpam-3759	198	4	converse	converse	NOUN
ejpam-3759	198	5	,	,	PUNCT
ejpam-3759	198	6	we	we	PRON
ejpam-3759	198	7	letb	letb	ADV
ejpam-3759	198	8	be	be	VERB
ejpam-3759	198	9	any	any	PRON
ejpam-3759	198	10	almost	almost	ADV
ejpam-3759	198	11	bi	bi	ADJ
ejpam-3759	198	12	-	-	ADJ
ejpam-3759	198	13	γ	γ	ADJ
ejpam-3759	198	14	-	-	PUNCT
ejpam-3759	198	15	ideal	ideal	ADJ
ejpam-3759	199	1	ofm	ofm	PROPN
ejpam-3759	200	1	.	.	PUNCT
ejpam-3759	201	1	follow	follow	VERB
ejpam-3759	201	2	by	by	ADP
ejpam-3759	201	3	theorem	theorem	NOUN
ejpam-3759	201	4	5	5	NUM
ejpam-3759	201	5	,	,	PUNCT
ejpam-3759	201	6	we	we	PRON
ejpam-3759	201	7	have	have	VERB
ejpam-3759	201	8	that	that	SCONJ
ejpam-3759	201	9	χb	χb	PROPN
ejpam-3759	201	10	is	be	AUX
ejpam-3759	201	11	a	a	DET
ejpam-3759	201	12	fuzzy	fuzzy	ADJ
ejpam-3759	201	13	almost	almost	ADV
ejpam-3759	201	14	bi	bi	ADJ
ejpam-3759	201	15	-	-	ADJ
ejpam-3759	201	16	γ	γ	ADJ
ejpam-3759	201	17	-	-	PUNCT
ejpam-3759	201	18	ideal	ideal	ADJ
ejpam-3759	201	19	ofm	ofm	PROPN
ejpam-3759	201	20	.	.	PUNCT
ejpam-3759	202	1	by	by	ADP
ejpam-3759	202	2	assumption	assumption	NOUN
ejpam-3759	202	3	,	,	PUNCT
ejpam-3759	202	4	we	we	PRON
ejpam-3759	202	5	getb	getb	VERB
ejpam-3759	202	6	=	=	SYM
ejpam-3759	202	7	supp(χb	supp(χb	PROPN
ejpam-3759	202	8	)	)	PUNCT
ejpam-3759	202	9	=	=	VERB
ejpam-3759	203	1	m.	m.	NOUN
ejpam-3759	203	2	this	this	PRON
ejpam-3759	203	3	implies	imply	VERB
ejpam-3759	203	4	that	that	SCONJ
ejpam-3759	203	5	m	m	NOUN
ejpam-3759	203	6	has	have	VERB
ejpam-3759	203	7	no	no	DET
ejpam-3759	203	8	proper	proper	ADJ
ejpam-3759	203	9	almost	almost	ADV
ejpam-3759	203	10	bi	bi	ADJ
ejpam-3759	203	11	-	-	ADJ
ejpam-3759	203	12	γ	γ	NOUN
ejpam-3759	203	13	-	-	PUNCT
ejpam-3759	203	14	ideals	ideal	NOUN
ejpam-3759	203	15	.	.	PUNCT
ejpam-3759	204	1	definition	definition	NOUN
ejpam-3759	204	2	6	6	NUM
ejpam-3759	204	3	.	.	PUNCT
ejpam-3759	205	1	let	let	VERB
ejpam-3759	205	2	m	m	PRON
ejpam-3759	205	3	be	be	AUX
ejpam-3759	205	4	a	a	DET
ejpam-3759	205	5	γ	γ	NOUN
ejpam-3759	205	6	-	-	PUNCT
ejpam-3759	205	7	semigroup	semigroup	NOUN
ejpam-3759	205	8	and	and	CCONJ
ejpam-3759	205	9	α	α	PRON
ejpam-3759	205	10	∈	∈	PROPN
ejpam-3759	205	11	γ	γ	X
ejpam-3759	205	12	.	.	PUNCT
ejpam-3759	206	1	(	(	PUNCT
ejpam-3759	206	2	1	1	X
ejpam-3759	206	3	)	)	PUNCT
ejpam-3759	206	4	an	an	DET
ejpam-3759	206	5	almost	almost	ADV
ejpam-3759	206	6	bi	bi	ADJ
ejpam-3759	206	7	-	-	ADJ
ejpam-3759	206	8	γ	γ	ADJ
ejpam-3759	206	9	-	-	PUNCT
ejpam-3759	206	10	ideal	ideal	ADJ
ejpam-3759	206	11	b	b	PROPN
ejpam-3759	206	12	of	of	ADP
ejpam-3759	206	13	m	m	PROPN
ejpam-3759	206	14	is	be	AUX
ejpam-3759	206	15	called	call	VERB
ejpam-3759	206	16	α	α	DET
ejpam-3759	206	17	-	-	NOUN
ejpam-3759	206	18	prime	prime	NOUN
ejpam-3759	206	19	if	if	SCONJ
ejpam-3759	206	20	xαy	xαy	PROPN
ejpam-3759	206	21	∈	∈	PROPN
ejpam-3759	206	22	b	b	PROPN
ejpam-3759	206	23	⇒	⇒	NOUN
ejpam-3759	206	24	x	x	PUNCT
ejpam-3759	206	25	∈	∈	PROPN
ejpam-3759	206	26	b	b	PROPN
ejpam-3759	206	27	or	or	CCONJ
ejpam-3759	206	28	y	y	PROPN
ejpam-3759	206	29	∈	∈	PROPN
ejpam-3759	206	30	b	b	PROPN
ejpam-3759	206	31	for	for	ADP
ejpam-3759	206	32	any	any	DET
ejpam-3759	206	33	x	x	NOUN
ejpam-3759	206	34	,	,	PUNCT
ejpam-3759	206	35	y	y	PROPN
ejpam-3759	206	36	∈m	∈m	NOUN
ejpam-3759	206	37	.	.	PUNCT
ejpam-3759	207	1	(	(	PUNCT
ejpam-3759	207	2	2	2	X
ejpam-3759	207	3	)	)	PUNCT
ejpam-3759	207	4	a	a	DET
ejpam-3759	207	5	fuzzy	fuzzy	ADJ
ejpam-3759	207	6	almost	almost	ADV
ejpam-3759	207	7	bi	bi	ADJ
ejpam-3759	207	8	-	-	ADJ
ejpam-3759	207	9	γ	γ	ADJ
ejpam-3759	207	10	-	-	PUNCT
ejpam-3759	207	11	ideal	ideal	ADJ
ejpam-3759	207	12	f	f	PROPN
ejpam-3759	207	13	of	of	ADP
ejpam-3759	207	14	m	m	PROPN
ejpam-3759	207	15	is	be	AUX
ejpam-3759	207	16	called	call	VERB
ejpam-3759	207	17	α	α	DET
ejpam-3759	207	18	-	-	NOUN
ejpam-3759	207	19	prime	prime	NOUN
ejpam-3759	207	20	if	if	SCONJ
ejpam-3759	207	21	f(xαy	f(xαy	NOUN
ejpam-3759	207	22	)	)	PUNCT
ejpam-3759	207	23	≤	≤	NUM
ejpam-3759	207	24	max{f(x	max{f(x	PROPN
ejpam-3759	207	25	)	)	PUNCT
ejpam-3759	207	26	,	,	PUNCT
ejpam-3759	207	27	f(y	f(y	NOUN
ejpam-3759	207	28	)	)	PUNCT
ejpam-3759	207	29	}	}	PUNCT
ejpam-3759	207	30	for	for	ADP
ejpam-3759	207	31	any	any	DET
ejpam-3759	207	32	x	x	NOUN
ejpam-3759	207	33	,	,	PUNCT
ejpam-3759	207	34	y	y	PROPN
ejpam-3759	207	35	∈m	∈m	NOUN
ejpam-3759	207	36	.	.	PUNCT
ejpam-3759	208	1	next	next	ADV
ejpam-3759	208	2	,	,	PUNCT
ejpam-3759	208	3	we	we	PRON
ejpam-3759	208	4	investigate	investigate	VERB
ejpam-3759	208	5	relationship	relationship	NOUN
ejpam-3759	208	6	between	between	ADP
ejpam-3759	208	7	α	α	NOUN
ejpam-3759	208	8	-	-	ADJ
ejpam-3759	208	9	prime	prime	ADJ
ejpam-3759	208	10	almost	almost	ADV
ejpam-3759	208	11	bi	bi	ADJ
ejpam-3759	208	12	-	-	ADJ
ejpam-3759	208	13	γ	γ	NOUN
ejpam-3759	208	14	-	-	PUNCT
ejpam-3759	208	15	ideals	ideal	NOUN
ejpam-3759	208	16	and	and	CCONJ
ejpam-3759	208	17	their	their	PRON
ejpam-3759	208	18	fuzzificaion	fuzzificaion	NOUN
ejpam-3759	208	19	.	.	PUNCT
ejpam-3759	209	1	theorem	theorem	VERB
ejpam-3759	209	2	8	8	NUM
ejpam-3759	209	3	.	.	PUNCT
ejpam-3759	210	1	a	a	DET
ejpam-3759	210	2	nonempty	nonempty	NOUN
ejpam-3759	210	3	subset	subset	VERB
ejpam-3759	210	4	a	a	PRON
ejpam-3759	210	5	of	of	ADP
ejpam-3759	210	6	a	a	DET
ejpam-3759	210	7	γ	γ	NOUN
ejpam-3759	210	8	-	-	PUNCT
ejpam-3759	210	9	semigroup	semigroup	NOUN
ejpam-3759	210	10	m	m	VERB
ejpam-3759	210	11	is	be	AUX
ejpam-3759	210	12	an	an	DET
ejpam-3759	210	13	α	α	NOUN
ejpam-3759	210	14	-	-	ADJ
ejpam-3759	210	15	prime	prime	ADJ
ejpam-3759	210	16	almost	almost	ADV
ejpam-3759	210	17	bi	bi	ADJ
ejpam-3759	210	18	-	-	ADJ
ejpam-3759	210	19	γ	γ	NOUN
ejpam-3759	210	20	-	-	NOUN
ejpam-3759	210	21	ideal	ideal	NOUN
ejpam-3759	210	22	of	of	ADP
ejpam-3759	210	23	m	m	PRON
ejpam-3759	210	24	if	if	SCONJ
ejpam-3759	211	1	and	and	CCONJ
ejpam-3759	211	2	only	only	ADV
ejpam-3759	211	3	if	if	SCONJ
ejpam-3759	211	4	χa	χa	PROPN
ejpam-3759	211	5	is	be	AUX
ejpam-3759	211	6	an	an	DET
ejpam-3759	211	7	α	α	NOUN
ejpam-3759	211	8	-	-	ADJ
ejpam-3759	211	9	prime	prime	ADJ
ejpam-3759	211	10	fuzzy	fuzzy	ADJ
ejpam-3759	211	11	almost	almost	ADV
ejpam-3759	211	12	bi	bi	ADJ
ejpam-3759	211	13	-	-	ADJ
ejpam-3759	211	14	γ	γ	NOUN
ejpam-3759	211	15	-	-	NOUN
ejpam-3759	211	16	ideal	ideal	NOUN
ejpam-3759	211	17	of	of	ADP
ejpam-3759	211	18	m	m	PROPN
ejpam-3759	211	19	.	.	PUNCT
ejpam-3759	212	1	proof	proof	NOUN
ejpam-3759	212	2	.	.	PUNCT
ejpam-3759	213	1	let	let	VERB
ejpam-3759	213	2	a	a	PRON
ejpam-3759	213	3	be	be	AUX
ejpam-3759	213	4	any	any	DET
ejpam-3759	213	5	α	α	NOUN
ejpam-3759	213	6	-	-	ADJ
ejpam-3759	213	7	prime	prime	ADJ
ejpam-3759	213	8	almost	almost	ADV
ejpam-3759	213	9	bi	bi	ADJ
ejpam-3759	213	10	-	-	ADJ
ejpam-3759	213	11	γ	γ	NOUN
ejpam-3759	213	12	-	-	NOUN
ejpam-3759	213	13	ideal	ideal	NOUN
ejpam-3759	213	14	of	of	ADP
ejpam-3759	213	15	m	m	PROPN
ejpam-3759	213	16	.	.	PUNCT
ejpam-3759	214	1	then	then	ADV
ejpam-3759	214	2	χa	χa	PROPN
ejpam-3759	214	3	is	be	AUX
ejpam-3759	214	4	a	a	DET
ejpam-3759	214	5	fuzzy	fuzzy	ADJ
ejpam-3759	214	6	almost	almost	ADV
ejpam-3759	214	7	bi	bi	ADJ
ejpam-3759	214	8	-	-	ADJ
ejpam-3759	214	9	γ	γ	NOUN
ejpam-3759	214	10	-	-	NOUN
ejpam-3759	214	11	ideal	ideal	NOUN
ejpam-3759	214	12	of	of	ADP
ejpam-3759	214	13	m	m	PRON
ejpam-3759	214	14	by	by	ADP
ejpam-3759	214	15	theorem	theorem	NOUN
ejpam-3759	214	16	5	5	NUM
ejpam-3759	214	17	.	.	PUNCT
ejpam-3759	215	1	let	let	VERB
ejpam-3759	215	2	x	x	PRON
ejpam-3759	215	3	and	and	CCONJ
ejpam-3759	215	4	y	y	PROPN
ejpam-3759	215	5	be	be	AUX
ejpam-3759	215	6	elements	element	NOUN
ejpam-3759	215	7	in	in	ADP
ejpam-3759	215	8	m	m	PROPN
ejpam-3759	215	9	.	.	PUNCT
ejpam-3759	216	1	if	if	SCONJ
ejpam-3759	216	2	xαy	xαy	PROPN
ejpam-3759	216	3	∈	∈	PROPN
ejpam-3759	216	4	a	a	PRON
ejpam-3759	216	5	,	,	PUNCT
ejpam-3759	216	6	then	then	ADV
ejpam-3759	216	7	x	x	PART
ejpam-3759	216	8	∈	∈	PROPN
ejpam-3759	216	9	a	a	PRON
ejpam-3759	216	10	or	or	CCONJ
ejpam-3759	216	11	y	y	PROPN
ejpam-3759	216	12	∈	∈	PROPN
ejpam-3759	216	13	a.	a.	NOUN
ejpam-3759	217	1	this	this	PRON
ejpam-3759	217	2	implies	imply	VERB
ejpam-3759	217	3	that	that	SCONJ
ejpam-3759	217	4	χa(xαy	χa(xαy	PROPN
ejpam-3759	217	5	)	)	PUNCT
ejpam-3759	217	6	=	=	SYM
ejpam-3759	217	7	1	1	NUM
ejpam-3759	217	8	≤	≤	NUM
ejpam-3759	217	9	max{χa(x	max{χa(x	NOUN
ejpam-3759	217	10	)	)	PUNCT
ejpam-3759	217	11	,	,	PUNCT
ejpam-3759	217	12	χa(y	χa(y	NOUN
ejpam-3759	217	13	)	)	PUNCT
ejpam-3759	217	14	}	}	PUNCT
ejpam-3759	217	15	.	.	PUNCT
ejpam-3759	218	1	if	if	SCONJ
ejpam-3759	218	2	xαy	xαy	PROPN
ejpam-3759	218	3	6∈	6∈	PROPN
ejpam-3759	218	4	a	a	PRON
ejpam-3759	218	5	,	,	PUNCT
ejpam-3759	218	6	then	then	ADV
ejpam-3759	218	7	χa(xαy	χa(xαy	PROPN
ejpam-3759	218	8	)	)	PUNCT
ejpam-3759	218	9	=	=	SYM
ejpam-3759	218	10	0	0	NUM
ejpam-3759	218	11	≤	≤	NUM
ejpam-3759	218	12	max{χa(x	max{χa(x	NOUN
ejpam-3759	218	13	)	)	PUNCT
ejpam-3759	218	14	,	,	PUNCT
ejpam-3759	218	15	χa(y	χa(y	NOUN
ejpam-3759	218	16	)	)	PUNCT
ejpam-3759	218	17	}	}	PUNCT
ejpam-3759	218	18	.	.	PUNCT
ejpam-3759	219	1	we	we	PRON
ejpam-3759	219	2	conclude	conclude	VERB
ejpam-3759	219	3	that	that	SCONJ
ejpam-3759	219	4	χa(xαy	χa(xαy	PROPN
ejpam-3759	219	5	)	)	PUNCT
ejpam-3759	219	6	≤	≤	NUM
ejpam-3759	219	7	max{χa(x	max{χa(x	NOUN
ejpam-3759	219	8	)	)	PUNCT
ejpam-3759	219	9	,	,	PUNCT
ejpam-3759	219	10	χa(y	χa(y	NOUN
ejpam-3759	219	11	)	)	PUNCT
ejpam-3759	219	12	}	}	PUNCT
ejpam-3759	219	13	for	for	ADP
ejpam-3759	219	14	all	all	DET
ejpam-3759	219	15	x	x	NOUN
ejpam-3759	219	16	,	,	PUNCT
ejpam-3759	219	17	y	y	PROPN
ejpam-3759	219	18	∈	∈	PROPN
ejpam-3759	219	19	m	m	VERB
ejpam-3759	219	20	.	.	PUNCT
ejpam-3759	220	1	therefore	therefore	ADV
ejpam-3759	220	2	,	,	PUNCT
ejpam-3759	220	3	χa	χa	PROPN
ejpam-3759	220	4	is	be	AUX
ejpam-3759	220	5	an	an	DET
ejpam-3759	220	6	α	α	NOUN
ejpam-3759	220	7	-	-	ADJ
ejpam-3759	220	8	prime	prime	ADJ
ejpam-3759	220	9	fuzzy	fuzzy	ADJ
ejpam-3759	220	10	almost	almost	ADV
ejpam-3759	220	11	bi	bi	ADJ
ejpam-3759	220	12	-	-	ADJ
ejpam-3759	220	13	γ	γ	NOUN
ejpam-3759	220	14	-	-	NOUN
ejpam-3759	220	15	ideal	ideal	NOUN
ejpam-3759	220	16	of	of	ADP
ejpam-3759	220	17	m	m	PROPN
ejpam-3759	220	18	.	.	PUNCT
ejpam-3759	221	1	to	to	PART
ejpam-3759	221	2	prove	prove	VERB
ejpam-3759	221	3	the	the	DET
ejpam-3759	221	4	converse	converse	NOUN
ejpam-3759	221	5	,	,	PUNCT
ejpam-3759	221	6	suppose	suppose	VERB
ejpam-3759	221	7	that	that	SCONJ
ejpam-3759	221	8	χa	χa	PROPN
ejpam-3759	221	9	is	be	AUX
ejpam-3759	221	10	an	an	DET
ejpam-3759	221	11	α	α	NOUN
ejpam-3759	221	12	-	-	ADJ
ejpam-3759	221	13	prime	prime	ADJ
ejpam-3759	221	14	fuzzy	fuzzy	ADJ
ejpam-3759	221	15	almost	almost	ADV
ejpam-3759	221	16	bi	bi	ADJ
ejpam-3759	221	17	-	-	ADJ
ejpam-3759	221	18	γ	γ	NOUN
ejpam-3759	221	19	-	-	NOUN
ejpam-3759	221	20	ideal	ideal	NOUN
ejpam-3759	221	21	of	of	ADP
ejpam-3759	221	22	m	m	PRON
ejpam-3759	221	23	.	.	PUNCT
ejpam-3759	222	1	by	by	ADP
ejpam-3759	222	2	theorem	theorem	NOUN
ejpam-3759	222	3	5	5	NUM
ejpam-3759	222	4	,	,	PUNCT
ejpam-3759	222	5	we	we	PRON
ejpam-3759	222	6	have	have	VERB
ejpam-3759	222	7	that	that	SCONJ
ejpam-3759	222	8	a	a	PRON
ejpam-3759	222	9	is	be	AUX
ejpam-3759	222	10	an	an	DET
ejpam-3759	222	11	almost	almost	ADV
ejpam-3759	222	12	bi	bi	ADJ
ejpam-3759	222	13	-	-	ADJ
ejpam-3759	222	14	γ	γ	NOUN
ejpam-3759	222	15	-	-	NOUN
ejpam-3759	222	16	ideal	ideal	NOUN
ejpam-3759	222	17	of	of	ADP
ejpam-3759	222	18	m	m	PROPN
ejpam-3759	222	19	.	.	PUNCT
ejpam-3759	223	1	let	let	VERB
ejpam-3759	223	2	x	x	PRON
ejpam-3759	223	3	and	and	CCONJ
ejpam-3759	223	4	y	y	PROPN
ejpam-3759	223	5	be	be	AUX
ejpam-3759	223	6	elements	element	NOUN
ejpam-3759	223	7	in	in	ADP
ejpam-3759	223	8	m	m	PRON
ejpam-3759	223	9	such	such	ADJ
ejpam-3759	223	10	that	that	SCONJ
ejpam-3759	223	11	xαy	xαy	PROPN
ejpam-3759	223	12	∈	∈	PROPN
ejpam-3759	223	13	a.	a.	NOUN
ejpam-3759	223	14	thus	thus	ADV
ejpam-3759	223	15	,	,	PUNCT
ejpam-3759	223	16	χa(xαy	χa(xαy	PROPN
ejpam-3759	223	17	)	)	PUNCT
ejpam-3759	223	18	=	=	SYM
ejpam-3759	224	1	1	1	X
ejpam-3759	224	2	.	.	PUNCT
ejpam-3759	224	3	by	by	ADP
ejpam-3759	224	4	assumption	assumption	NOUN
ejpam-3759	224	5	,	,	PUNCT
ejpam-3759	224	6	we	we	PRON
ejpam-3759	224	7	have	have	VERB
ejpam-3759	224	8	that	that	DET
ejpam-3759	224	9	χa(xαy	χa(xαy	PROPN
ejpam-3759	224	10	)	)	PUNCT
ejpam-3759	224	11	≤	≤	NUM
ejpam-3759	224	12	max{χa(x	max{χa(x	NOUN
ejpam-3759	224	13	)	)	PUNCT
ejpam-3759	224	14	,	,	PUNCT
ejpam-3759	224	15	χa(y	χa(y	NOUN
ejpam-3759	224	16	)	)	PUNCT
ejpam-3759	224	17	}	}	PUNCT
ejpam-3759	224	18	.	.	PUNCT
ejpam-3759	225	1	therefore	therefore	ADV
ejpam-3759	225	2	,	,	PUNCT
ejpam-3759	225	3	max{χa(x	max{χa(x	NOUN
ejpam-3759	225	4	)	)	PUNCT
ejpam-3759	225	5	,	,	PUNCT
ejpam-3759	225	6	χa(y	χa(y	NOUN
ejpam-3759	225	7	)	)	PUNCT
ejpam-3759	225	8	}	}	PUNCT
ejpam-3759	226	1	=	=	SYM
ejpam-3759	226	2	1	1	X
ejpam-3759	226	3	.	.	X
ejpam-3759	227	1	we	we	PRON
ejpam-3759	227	2	can	can	AUX
ejpam-3759	227	3	conclude	conclude	VERB
ejpam-3759	227	4	that	that	SCONJ
ejpam-3759	227	5	x	x	PUNCT
ejpam-3759	227	6	∈	∈	PROPN
ejpam-3759	227	7	a	a	PRON
ejpam-3759	227	8	or	or	CCONJ
ejpam-3759	227	9	y	y	PROPN
ejpam-3759	227	10	∈	∈	PROPN
ejpam-3759	227	11	a.	a.	NOUN
ejpam-3759	227	12	hence	hence	ADV
ejpam-3759	227	13	,	,	PUNCT
ejpam-3759	227	14	a	a	PRON
ejpam-3759	227	15	is	be	AUX
ejpam-3759	227	16	an	an	DET
ejpam-3759	227	17	α	α	NOUN
ejpam-3759	227	18	-	-	ADJ
ejpam-3759	227	19	prime	prime	ADJ
ejpam-3759	227	20	almost	almost	ADV
ejpam-3759	227	21	bi	bi	ADJ
ejpam-3759	227	22	-	-	ADJ
ejpam-3759	227	23	γ	γ	NOUN
ejpam-3759	227	24	-	-	NOUN
ejpam-3759	227	25	ideal	ideal	NOUN
ejpam-3759	227	26	of	of	ADP
ejpam-3759	227	27	m	m	PROPN
ejpam-3759	227	28	.	.	PUNCT
ejpam-3759	228	1	r.	r.	PROPN
ejpam-3759	228	2	chinram	chinram	PROPN
ejpam-3759	228	3	et	et	PROPN
ejpam-3759	228	4	al	al	PROPN
ejpam-3759	228	5	.	.	PUNCT
ejpam-3759	228	6	/	/	SYM
ejpam-3759	228	7	eur	eur	PROPN
ejpam-3759	228	8	.	.	PUNCT
ejpam-3759	229	1	j.	j.	PROPN
ejpam-3759	229	2	pure	pure	PROPN
ejpam-3759	229	3	appl	appl	PROPN
ejpam-3759	229	4	.	.	PROPN
ejpam-3759	229	5	math	math	PROPN
ejpam-3759	229	6	,	,	PUNCT
ejpam-3759	229	7	13	13	NUM
ejpam-3759	229	8	(	(	PUNCT
ejpam-3759	229	9	3	3	NUM
ejpam-3759	229	10	)	)	PUNCT
ejpam-3759	229	11	(	(	PUNCT
ejpam-3759	229	12	2020	2020	NUM
ejpam-3759	229	13	)	)	PUNCT
ejpam-3759	229	14	,	,	PUNCT
ejpam-3759	229	15	620	620	NUM
ejpam-3759	229	16	-	-	SYM
ejpam-3759	229	17	630	630	NUM
ejpam-3759	229	18	628	628	NUM
ejpam-3759	229	19	definition	definition	NOUN
ejpam-3759	229	20	7	7	NUM
ejpam-3759	229	21	.	.	PUNCT
ejpam-3759	230	1	let	let	VERB
ejpam-3759	230	2	m	m	PRON
ejpam-3759	230	3	be	be	AUX
ejpam-3759	230	4	a	a	DET
ejpam-3759	230	5	γ	γ	NOUN
ejpam-3759	230	6	-	-	PUNCT
ejpam-3759	230	7	semigroup	semigroup	NOUN
ejpam-3759	230	8	and	and	CCONJ
ejpam-3759	230	9	α	α	PRON
ejpam-3759	230	10	∈	∈	PROPN
ejpam-3759	230	11	γ	γ	X
ejpam-3759	230	12	.	.	PUNCT
ejpam-3759	231	1	(	(	PUNCT
ejpam-3759	231	2	1	1	X
ejpam-3759	231	3	)	)	PUNCT
ejpam-3759	231	4	an	an	DET
ejpam-3759	231	5	almost	almost	ADV
ejpam-3759	231	6	bi	bi	ADJ
ejpam-3759	231	7	-	-	ADJ
ejpam-3759	231	8	γ	γ	NOUN
ejpam-3759	231	9	-	-	NOUN
ejpam-3759	231	10	ideal	ideal	NOUN
ejpam-3759	231	11	a	a	PRON
ejpam-3759	231	12	of	of	ADP
ejpam-3759	231	13	m	m	PROPN
ejpam-3759	231	14	is	be	AUX
ejpam-3759	231	15	called	call	VERB
ejpam-3759	231	16	α	α	DET
ejpam-3759	231	17	-	-	ADJ
ejpam-3759	231	18	semiprime	semiprime	NOUN
ejpam-3759	231	19	if	if	SCONJ
ejpam-3759	231	20	mαm	mαm	ADV
ejpam-3759	231	21	∈	∈	PROPN
ejpam-3759	231	22	a⇒	a⇒	NOUN
ejpam-3759	231	23	m	m	VERB
ejpam-3759	231	24	∈	∈	PROPN
ejpam-3759	231	25	a	a	PRON
ejpam-3759	231	26	for	for	ADP
ejpam-3759	231	27	all	all	DET
ejpam-3759	231	28	m	m	NOUN
ejpam-3759	231	29	∈m	∈m	NOUN
ejpam-3759	231	30	.	.	PUNCT
ejpam-3759	232	1	(	(	PUNCT
ejpam-3759	232	2	2	2	X
ejpam-3759	232	3	)	)	PUNCT
ejpam-3759	232	4	a	a	DET
ejpam-3759	232	5	fuzzy	fuzzy	ADJ
ejpam-3759	232	6	almost	almost	ADV
ejpam-3759	232	7	bi	bi	ADJ
ejpam-3759	232	8	-	-	ADJ
ejpam-3759	232	9	γ	γ	ADJ
ejpam-3759	232	10	-	-	PUNCT
ejpam-3759	232	11	ideal	ideal	ADJ
ejpam-3759	232	12	f	f	PROPN
ejpam-3759	232	13	of	of	ADP
ejpam-3759	232	14	m	m	PROPN
ejpam-3759	232	15	is	be	AUX
ejpam-3759	232	16	called	call	VERB
ejpam-3759	232	17	α	α	DET
ejpam-3759	232	18	-	-	ADJ
ejpam-3759	232	19	semiprime	semiprime	NOUN
ejpam-3759	232	20	if	if	SCONJ
ejpam-3759	232	21	f(mαm	f(mαm	NOUN
ejpam-3759	232	22	)	)	PUNCT
ejpam-3759	232	23	≤	≤	NOUN
ejpam-3759	232	24	f(m	f(m	PROPN
ejpam-3759	232	25	)	)	PUNCT
ejpam-3759	232	26	for	for	ADP
ejpam-3759	232	27	all	all	DET
ejpam-3759	232	28	m	m	NOUN
ejpam-3759	232	29	∈m	∈m	NOUN
ejpam-3759	232	30	.	.	PUNCT
ejpam-3759	233	1	finally	finally	ADV
ejpam-3759	233	2	,	,	PUNCT
ejpam-3759	233	3	we	we	PRON
ejpam-3759	233	4	give	give	VERB
ejpam-3759	233	5	relationship	relationship	NOUN
ejpam-3759	233	6	between	between	ADP
ejpam-3759	233	7	α	α	NOUN
ejpam-3759	233	8	-	-	PUNCT
ejpam-3759	233	9	semiprime	semiprime	NOUN
ejpam-3759	233	10	almost	almost	ADV
ejpam-3759	233	11	bi	bi	ADJ
ejpam-3759	233	12	-	-	ADJ
ejpam-3759	233	13	γ	γ	NOUN
ejpam-3759	233	14	-	-	PUNCT
ejpam-3759	233	15	ideals	ideal	NOUN
ejpam-3759	233	16	and	and	CCONJ
ejpam-3759	233	17	their	their	PRON
ejpam-3759	233	18	fuzzification	fuzzification	NOUN
ejpam-3759	233	19	.	.	PUNCT
ejpam-3759	234	1	theorem	theorem	VERB
ejpam-3759	234	2	9	9	NUM
ejpam-3759	234	3	.	.	PUNCT
ejpam-3759	235	1	a	a	DET
ejpam-3759	235	2	nonempty	nonempty	NOUN
ejpam-3759	235	3	subset	subset	VERB
ejpam-3759	235	4	a	a	PRON
ejpam-3759	235	5	of	of	ADP
ejpam-3759	235	6	a	a	DET
ejpam-3759	235	7	γ	γ	NOUN
ejpam-3759	235	8	-	-	PUNCT
ejpam-3759	235	9	semigroup	semigroup	NOUN
ejpam-3759	235	10	m	m	VERB
ejpam-3759	235	11	is	be	AUX
ejpam-3759	235	12	an	an	DET
ejpam-3759	235	13	α	α	NOUN
ejpam-3759	235	14	-	-	ADJ
ejpam-3759	235	15	semiprime	semiprime	ADJ
ejpam-3759	235	16	almost	almost	ADV
ejpam-3759	235	17	bi	bi	NOUN
ejpam-3759	235	18	-	-	NOUN
ejpam-3759	235	19	γideal	γideal	NOUN
ejpam-3759	235	20	of	of	ADP
ejpam-3759	235	21	m	m	NOUN
ejpam-3759	235	22	if	if	SCONJ
ejpam-3759	236	1	and	and	CCONJ
ejpam-3759	236	2	only	only	ADV
ejpam-3759	236	3	if	if	SCONJ
ejpam-3759	236	4	χa	χa	PROPN
ejpam-3759	236	5	is	be	AUX
ejpam-3759	236	6	an	an	DET
ejpam-3759	236	7	α	α	PRON
ejpam-3759	236	8	-	-	ADJ
ejpam-3759	236	9	semiprime	semiprime	ADJ
ejpam-3759	236	10	fuzzy	fuzzy	ADJ
ejpam-3759	236	11	almost	almost	ADV
ejpam-3759	236	12	bi	bi	ADJ
ejpam-3759	236	13	-	-	ADJ
ejpam-3759	236	14	γ	γ	NOUN
ejpam-3759	236	15	-	-	NOUN
ejpam-3759	236	16	ideal	ideal	NOUN
ejpam-3759	236	17	of	of	ADP
ejpam-3759	236	18	m	m	PROPN
ejpam-3759	236	19	.	.	PUNCT
ejpam-3759	237	1	proof	proof	NOUN
ejpam-3759	237	2	.	.	PUNCT
ejpam-3759	238	1	let	let	VERB
ejpam-3759	238	2	a	a	PRON
ejpam-3759	238	3	be	be	AUX
ejpam-3759	238	4	an	an	DET
ejpam-3759	238	5	α	α	NOUN
ejpam-3759	238	6	-	-	ADJ
ejpam-3759	238	7	semiprime	semiprime	ADJ
ejpam-3759	238	8	almost	almost	ADV
ejpam-3759	238	9	bi	bi	ADJ
ejpam-3759	238	10	-	-	ADJ
ejpam-3759	238	11	γ	γ	NOUN
ejpam-3759	238	12	-	-	NOUN
ejpam-3759	238	13	ideal	ideal	NOUN
ejpam-3759	238	14	of	of	ADP
ejpam-3759	238	15	m	m	PRON
ejpam-3759	238	16	.	.	PUNCT
ejpam-3759	239	1	by	by	ADP
ejpam-3759	239	2	theorem	theorem	NOUN
ejpam-3759	239	3	5	5	NUM
ejpam-3759	239	4	,	,	PUNCT
ejpam-3759	239	5	χa	χa	PROPN
ejpam-3759	239	6	is	be	AUX
ejpam-3759	239	7	a	a	DET
ejpam-3759	239	8	fuzzy	fuzzy	ADJ
ejpam-3759	239	9	almost	almost	ADV
ejpam-3759	239	10	bi	bi	ADJ
ejpam-3759	239	11	-	-	ADJ
ejpam-3759	239	12	γ	γ	NOUN
ejpam-3759	239	13	-	-	NOUN
ejpam-3759	239	14	ideal	ideal	NOUN
ejpam-3759	239	15	of	of	ADP
ejpam-3759	239	16	m	m	PROPN
ejpam-3759	239	17	.	.	PUNCT
ejpam-3759	240	1	let	let	VERB
ejpam-3759	240	2	m	m	PRON
ejpam-3759	240	3	∈	∈	VERB
ejpam-3759	240	4	m	m	NOUN
ejpam-3759	240	5	.	.	PUNCT
ejpam-3759	241	1	if	if	SCONJ
ejpam-3759	241	2	mαm	mαm	X
ejpam-3759	241	3	∈	∈	PROPN
ejpam-3759	241	4	a	a	DET
ejpam-3759	241	5	,	,	PUNCT
ejpam-3759	241	6	then	then	ADV
ejpam-3759	241	7	m	m	VERB
ejpam-3759	241	8	∈	∈	NOUN
ejpam-3759	241	9	a.	a.	NOUN
ejpam-3759	241	10	so	so	ADV
ejpam-3759	241	11	,	,	PUNCT
ejpam-3759	241	12	χa(m	χa(m	X
ejpam-3759	241	13	)	)	PUNCT
ejpam-3759	241	14	=	=	SYM
ejpam-3759	242	1	1	1	X
ejpam-3759	242	2	.	.	PUNCT
ejpam-3759	242	3	hence	hence	ADV
ejpam-3759	242	4	,	,	PUNCT
ejpam-3759	242	5	χa(mαm	χa(mαm	CCONJ
ejpam-3759	242	6	)	)	PUNCT
ejpam-3759	242	7	≤	≤	NOUN
ejpam-3759	242	8	χa(m	χa(m	NOUN
ejpam-3759	242	9	)	)	PUNCT
ejpam-3759	242	10	.	.	PUNCT
ejpam-3759	243	1	if	if	SCONJ
ejpam-3759	243	2	mαm	mαm	PROPN
ejpam-3759	243	3	6∈	6∈	PROPN
ejpam-3759	243	4	a	a	PRON
ejpam-3759	243	5	,	,	PUNCT
ejpam-3759	243	6	then	then	ADV
ejpam-3759	243	7	χa(mαm	χa(mαm	ADJ
ejpam-3759	243	8	)	)	PUNCT
ejpam-3759	243	9	=	=	SYM
ejpam-3759	243	10	0	0	NUM
ejpam-3759	243	11	≤	≤	NOUN
ejpam-3759	243	12	χa(m	χa(m	NOUN
ejpam-3759	243	13	)	)	PUNCT
ejpam-3759	243	14	.	.	PUNCT
ejpam-3759	244	1	by	by	ADP
ejpam-3759	244	2	both	both	DET
ejpam-3759	244	3	cases	case	NOUN
ejpam-3759	244	4	,	,	PUNCT
ejpam-3759	244	5	we	we	PRON
ejpam-3759	244	6	conclude	conclude	VERB
ejpam-3759	244	7	that	that	PRON
ejpam-3759	244	8	χa(mαm	χa(mαm	NOUN
ejpam-3759	244	9	)	)	PUNCT
ejpam-3759	244	10	≤	≤	NOUN
ejpam-3759	244	11	χa(m	χa(m	NOUN
ejpam-3759	244	12	)	)	PUNCT
ejpam-3759	244	13	for	for	ADP
ejpam-3759	244	14	all	all	DET
ejpam-3759	244	15	m	m	NOUN
ejpam-3759	244	16	∈	∈	NOUN
ejpam-3759	244	17	m	m	NOUN
ejpam-3759	244	18	.	.	PUNCT
ejpam-3759	245	1	thus	thus	ADV
ejpam-3759	245	2	,	,	PUNCT
ejpam-3759	245	3	χa	χa	PROPN
ejpam-3759	245	4	is	be	AUX
ejpam-3759	245	5	an	an	DET
ejpam-3759	245	6	α	α	PRON
ejpam-3759	245	7	-	-	ADJ
ejpam-3759	245	8	semiprime	semiprime	ADJ
ejpam-3759	245	9	fuzzy	fuzzy	ADJ
ejpam-3759	245	10	almost	almost	ADV
ejpam-3759	245	11	bi	bi	ADJ
ejpam-3759	245	12	-	-	ADJ
ejpam-3759	245	13	γ	γ	NOUN
ejpam-3759	245	14	-	-	NOUN
ejpam-3759	245	15	ideal	ideal	NOUN
ejpam-3759	245	16	of	of	ADP
ejpam-3759	245	17	m	m	PRON
ejpam-3759	245	18	.	.	PUNCT
ejpam-3759	246	1	conversely	conversely	ADV
ejpam-3759	246	2	,	,	PUNCT
ejpam-3759	246	3	assume	assume	VERB
ejpam-3759	246	4	that	that	SCONJ
ejpam-3759	246	5	χa	χa	PROPN
ejpam-3759	246	6	is	be	AUX
ejpam-3759	246	7	an	an	DET
ejpam-3759	246	8	α	α	PRON
ejpam-3759	246	9	-	-	ADJ
ejpam-3759	246	10	semiprime	semiprime	ADJ
ejpam-3759	246	11	fuzzy	fuzzy	ADJ
ejpam-3759	246	12	almost	almost	ADV
ejpam-3759	246	13	bi	bi	ADJ
ejpam-3759	246	14	-	-	ADJ
ejpam-3759	246	15	γ	γ	NOUN
ejpam-3759	246	16	-	-	NOUN
ejpam-3759	246	17	ideal	ideal	NOUN
ejpam-3759	246	18	of	of	ADP
ejpam-3759	246	19	m	m	PRON
ejpam-3759	246	20	.	.	PUNCT
ejpam-3759	247	1	by	by	ADP
ejpam-3759	247	2	theorem	theorem	NOUN
ejpam-3759	247	3	5	5	NUM
ejpam-3759	247	4	,	,	PUNCT
ejpam-3759	247	5	we	we	PRON
ejpam-3759	247	6	have	have	VERB
ejpam-3759	247	7	that	that	SCONJ
ejpam-3759	247	8	a	a	PRON
ejpam-3759	247	9	is	be	AUX
ejpam-3759	247	10	an	an	DET
ejpam-3759	247	11	almost	almost	ADV
ejpam-3759	247	12	bi	bi	ADJ
ejpam-3759	247	13	-	-	ADJ
ejpam-3759	247	14	γ	γ	NOUN
ejpam-3759	247	15	-	-	NOUN
ejpam-3759	247	16	ideal	ideal	NOUN
ejpam-3759	247	17	of	of	ADP
ejpam-3759	247	18	m	m	PROPN
ejpam-3759	247	19	.	.	PUNCT
ejpam-3759	248	1	let	let	VERB
ejpam-3759	248	2	m	m	PRON
ejpam-3759	248	3	∈	∈	VERB
ejpam-3759	248	4	m	m	AUX
ejpam-3759	248	5	be	be	VERB
ejpam-3759	248	6	such	such	ADJ
ejpam-3759	248	7	that	that	DET
ejpam-3759	248	8	mαm	mαm	ADJ
ejpam-3759	248	9	∈	∈	PROPN
ejpam-3759	248	10	a.	a.	NOUN
ejpam-3759	248	11	thus	thus	ADV
ejpam-3759	248	12	χa(mαm	χa(mαm	X
ejpam-3759	248	13	)	)	PUNCT
ejpam-3759	248	14	=	=	SYM
ejpam-3759	249	1	1	1	X
ejpam-3759	249	2	.	.	PUNCT
ejpam-3759	249	3	by	by	ADP
ejpam-3759	249	4	assumption	assumption	NOUN
ejpam-3759	249	5	,	,	PUNCT
ejpam-3759	249	6	we	we	PRON
ejpam-3759	249	7	have	have	VERB
ejpam-3759	249	8	that	that	DET
ejpam-3759	249	9	χa(mαm	χa(mαm	NOUN
ejpam-3759	249	10	)	)	PUNCT
ejpam-3759	249	11	≤	≤	NOUN
ejpam-3759	249	12	χa(m	χa(m	NOUN
ejpam-3759	249	13	)	)	PUNCT
ejpam-3759	249	14	.	.	PUNCT
ejpam-3759	250	1	since	since	SCONJ
ejpam-3759	250	2	χa(mαm	χa(mαm	PROPN
ejpam-3759	250	3	)	)	PUNCT
ejpam-3759	250	4	=	=	SYM
ejpam-3759	250	5	1	1	NUM
ejpam-3759	250	6	,	,	PUNCT
ejpam-3759	250	7	it	it	PRON
ejpam-3759	250	8	follows	follow	VERB
ejpam-3759	250	9	that	that	SCONJ
ejpam-3759	250	10	χa(m	χa(m	ADV
ejpam-3759	250	11	)	)	PUNCT
ejpam-3759	250	12	=	=	SYM
ejpam-3759	251	1	1	1	X
ejpam-3759	251	2	.	.	PUNCT
ejpam-3759	251	3	therefore	therefore	ADV
ejpam-3759	251	4	,	,	PUNCT
ejpam-3759	251	5	m	m	PROPN
ejpam-3759	251	6	∈	∈	NOUN
ejpam-3759	251	7	a.	a.	NOUN
ejpam-3759	251	8	consequently	consequently	ADV
ejpam-3759	251	9	,	,	PUNCT
ejpam-3759	251	10	a	a	PRON
ejpam-3759	251	11	is	be	AUX
ejpam-3759	251	12	an	an	DET
ejpam-3759	251	13	α	α	NOUN
ejpam-3759	251	14	-	-	ADJ
ejpam-3759	251	15	semiprime	semiprime	ADJ
ejpam-3759	251	16	almost	almost	ADV
ejpam-3759	251	17	bi	bi	ADJ
ejpam-3759	251	18	-	-	ADJ
ejpam-3759	251	19	γ	γ	NOUN
ejpam-3759	251	20	-	-	NOUN
ejpam-3759	251	21	ideal	ideal	NOUN
ejpam-3759	251	22	of	of	ADP
ejpam-3759	251	23	m	m	PROPN
ejpam-3759	251	24	.	.	PUNCT
ejpam-3759	252	1	5	5	X
ejpam-3759	252	2	.	.	X
ejpam-3759	252	3	conclusion	conclusion	NOUN
ejpam-3759	252	4	in	in	ADP
ejpam-3759	252	5	this	this	DET
ejpam-3759	252	6	paper	paper	NOUN
ejpam-3759	252	7	,	,	PUNCT
ejpam-3759	252	8	we	we	PRON
ejpam-3759	252	9	define	define	VERB
ejpam-3759	252	10	almost	almost	ADV
ejpam-3759	252	11	bi	bi	ADJ
ejpam-3759	252	12	-	-	ADJ
ejpam-3759	252	13	γ	γ	NOUN
ejpam-3759	252	14	-	-	PUNCT
ejpam-3759	252	15	ideals	ideal	NOUN
ejpam-3759	252	16	and	and	CCONJ
ejpam-3759	252	17	their	their	PRON
ejpam-3759	252	18	fuzzification	fuzzification	NOUN
ejpam-3759	252	19	of	of	ADP
ejpam-3759	252	20	γ	γ	NOUN
ejpam-3759	252	21	-	-	PUNCT
ejpam-3759	252	22	semigroups	semigroup	NOUN
ejpam-3759	252	23	.	.	PUNCT
ejpam-3759	253	1	every	every	DET
ejpam-3759	253	2	bi	bi	ADJ
ejpam-3759	253	3	-	-	ADJ
ejpam-3759	253	4	γ	γ	NOUN
ejpam-3759	253	5	-	-	PUNCT
ejpam-3759	253	6	ideal	ideal	NOUN
ejpam-3759	253	7	is	be	AUX
ejpam-3759	253	8	an	an	DET
ejpam-3759	253	9	almost	almost	ADV
ejpam-3759	253	10	bi	bi	ADJ
ejpam-3759	253	11	-	-	ADJ
ejpam-3759	253	12	γ	γ	NOUN
ejpam-3759	253	13	-	-	ADJ
ejpam-3759	253	14	ideal	ideal	NOUN
ejpam-3759	253	15	but	but	CCONJ
ejpam-3759	253	16	the	the	DET
ejpam-3759	253	17	converse	converse	NOUN
ejpam-3759	253	18	is	be	AUX
ejpam-3759	253	19	not	not	PART
ejpam-3759	253	20	true	true	ADJ
ejpam-3759	253	21	in	in	ADP
ejpam-3759	253	22	general	general	ADJ
ejpam-3759	253	23	.	.	PUNCT
ejpam-3759	254	1	we	we	PRON
ejpam-3759	254	2	show	show	VERB
ejpam-3759	254	3	that	that	SCONJ
ejpam-3759	254	4	the	the	DET
ejpam-3759	254	5	union	union	NOUN
ejpam-3759	254	6	of	of	ADP
ejpam-3759	254	7	two	two	NUM
ejpam-3759	254	8	almost	almost	ADV
ejpam-3759	254	9	bi	bi	ADJ
ejpam-3759	254	10	-	-	ADJ
ejpam-3759	254	11	γ	γ	NOUN
ejpam-3759	254	12	-	-	PUNCT
ejpam-3759	254	13	ideals	ideal	NOUN
ejpam-3759	254	14	is	be	AUX
ejpam-3759	254	15	also	also	ADV
ejpam-3759	254	16	an	an	DET
ejpam-3759	254	17	almost	almost	ADV
ejpam-3759	254	18	bi	bi	ADJ
ejpam-3759	254	19	-	-	ADJ
ejpam-3759	254	20	γ	γ	NOUN
ejpam-3759	254	21	-	-	PUNCT
ejpam-3759	254	22	ideal	ideal	NOUN
ejpam-3759	254	23	.	.	PUNCT
ejpam-3759	255	1	however	however	ADV
ejpam-3759	255	2	,	,	PUNCT
ejpam-3759	255	3	it	it	PRON
ejpam-3759	255	4	is	be	AUX
ejpam-3759	255	5	not	not	PART
ejpam-3759	255	6	generally	generally	ADV
ejpam-3759	255	7	true	true	ADJ
ejpam-3759	255	8	in	in	ADP
ejpam-3759	255	9	case	case	NOUN
ejpam-3759	255	10	the	the	DET
ejpam-3759	255	11	intersection	intersection	NOUN
ejpam-3759	255	12	.	.	PUNCT
ejpam-3759	256	1	similarly	similarly	ADV
ejpam-3759	256	2	,	,	PUNCT
ejpam-3759	256	3	we	we	PRON
ejpam-3759	256	4	have	have	VERB
ejpam-3759	256	5	that	that	SCONJ
ejpam-3759	256	6	the	the	DET
ejpam-3759	256	7	union	union	NOUN
ejpam-3759	256	8	of	of	ADP
ejpam-3759	256	9	two	two	NUM
ejpam-3759	256	10	fuzzy	fuzzy	ADJ
ejpam-3759	256	11	almost	almost	ADV
ejpam-3759	256	12	bi	bi	ADJ
ejpam-3759	256	13	-	-	ADJ
ejpam-3759	256	14	γ	γ	NOUN
ejpam-3759	256	15	-	-	PUNCT
ejpam-3759	256	16	ideals	ideal	NOUN
ejpam-3759	256	17	is	be	AUX
ejpam-3759	256	18	also	also	ADV
ejpam-3759	256	19	a	a	DET
ejpam-3759	256	20	fuzzy	fuzzy	ADJ
ejpam-3759	256	21	almost	almost	ADV
ejpam-3759	256	22	bi	bi	ADJ
ejpam-3759	256	23	-	-	ADJ
ejpam-3759	256	24	γ	γ	NOUN
ejpam-3759	256	25	-	-	NOUN
ejpam-3759	256	26	ideal	ideal	NOUN
ejpam-3759	257	1	but	but	CCONJ
ejpam-3759	257	2	it	it	PRON
ejpam-3759	257	3	is	be	AUX
ejpam-3759	257	4	not	not	PART
ejpam-3759	257	5	generally	generally	ADV
ejpam-3759	257	6	true	true	ADJ
ejpam-3759	257	7	in	in	ADP
ejpam-3759	257	8	case	case	NOUN
ejpam-3759	257	9	the	the	DET
ejpam-3759	257	10	intersection	intersection	NOUN
ejpam-3759	257	11	.	.	PUNCT
ejpam-3759	258	1	moreover	moreover	ADV
ejpam-3759	258	2	,	,	PUNCT
ejpam-3759	258	3	the	the	DET
ejpam-3759	258	4	relationships	relationship	NOUN
ejpam-3759	258	5	between	between	ADP
ejpam-3759	258	6	almost	almost	ADV
ejpam-3759	258	7	bi	bi	NOUN
ejpam-3759	258	8	-	-	ADJ
ejpam-3759	258	9	γ	γ	NOUN
ejpam-3759	258	10	-	-	PUNCT
ejpam-3759	258	11	ideals	ideal	NOUN
ejpam-3759	258	12	and	and	CCONJ
ejpam-3759	258	13	their	their	PRON
ejpam-3759	258	14	fuzzification	fuzzification	NOUN
ejpam-3759	258	15	were	be	AUX
ejpam-3759	258	16	shown	show	VERB
ejpam-3759	258	17	in	in	ADP
ejpam-3759	258	18	section	section	NOUN
ejpam-3759	258	19	4	4	NUM
ejpam-3759	258	20	.	.	PUNCT
ejpam-3759	259	1	acknowledgements	acknowledgement	NOUN
ejpam-3759	259	2	this	this	DET
ejpam-3759	259	3	work	work	NOUN
ejpam-3759	259	4	was	be	AUX
ejpam-3759	259	5	supported	support	VERB
ejpam-3759	259	6	by	by	ADP
ejpam-3759	259	7	the	the	DET
ejpam-3759	259	8	faculty	faculty	NOUN
ejpam-3759	259	9	of	of	ADP
ejpam-3759	259	10	sciences	sciences	PROPN
ejpam-3759	259	11	research	research	PROPN
ejpam-3759	259	12	fund	fund	NOUN
ejpam-3759	259	13	,	,	PUNCT
ejpam-3759	259	14	prince	prince	NOUN
ejpam-3759	259	15	of	of	ADP
ejpam-3759	259	16	songkla	songkla	PROPN
ejpam-3759	259	17	university	university	PROPN
ejpam-3759	259	18	,	,	PUNCT
ejpam-3759	259	19	contract	contract	NOUN
ejpam-3759	259	20	no	no	INTJ
ejpam-3759	259	21	.	.	NOUN
ejpam-3759	260	1	1	1	NUM
ejpam-3759	260	2	-	-	SYM
ejpam-3759	260	3	2562	2562	NUM
ejpam-3759	260	4	-	-	PUNCT
ejpam-3759	260	5	02	02	NUM
ejpam-3759	260	6	-	-	PUNCT
ejpam-3759	260	7	013	013	NUM
ejpam-3759	260	8	.	.	PUNCT
ejpam-3759	261	1	we	we	PRON
ejpam-3759	261	2	would	would	AUX
ejpam-3759	261	3	like	like	VERB
ejpam-3759	261	4	to	to	PART
ejpam-3759	261	5	thank	thank	VERB
ejpam-3759	261	6	the	the	DET
ejpam-3759	261	7	reviewers	reviewer	NOUN
ejpam-3759	261	8	for	for	ADP
ejpam-3759	261	9	their	their	PRON
ejpam-3759	261	10	comments	comment	NOUN
ejpam-3759	261	11	and	and	CCONJ
ejpam-3759	261	12	suggestions	suggestion	NOUN
ejpam-3759	261	13	.	.	PUNCT
ejpam-3759	262	1	references	reference	NOUN
ejpam-3759	262	2	629	629	NUM
ejpam-3759	262	3	references	reference	NOUN
ejpam-3759	262	4	[	[	X
ejpam-3759	262	5	1	1	NUM
ejpam-3759	262	6	]	]	PUNCT
ejpam-3759	262	7	m.	m.	NOUN
ejpam-3759	262	8	a.	a.	NOUN
ejpam-3759	262	9	ansari	ansari	PROPN
ejpam-3759	262	10	.	.	PUNCT
ejpam-3759	263	1	roughness	roughness	NOUN
ejpam-3759	263	2	applied	apply	VERB
ejpam-3759	263	3	to	to	ADP
ejpam-3759	263	4	generalized	generalize	VERB
ejpam-3759	263	5	γ	γ	NOUN
ejpam-3759	263	6	-	-	NOUN
ejpam-3759	263	7	ideals	ideal	NOUN
ejpam-3759	263	8	of	of	ADP
ejpam-3759	263	9	ordered	order	VERB
ejpam-3759	263	10	la	la	PROPN
ejpam-3759	263	11	γ	γ	X
ejpam-3759	263	12	-	-	NOUN
ejpam-3759	263	13	ideals	ideal	NOUN
ejpam-3759	263	14	.	.	PUNCT
ejpam-3759	264	1	commun	commun	PROPN
ejpam-3759	264	2	.	.	PUNCT
ejpam-3759	265	1	math	math	PROPN
ejpam-3759	265	2	.	.	PUNCT
ejpam-3759	266	1	appl	appl	PROPN
ejpam-3759	266	2	.	.	PROPN
ejpam-3759	266	3	,	,	PUNCT
ejpam-3759	266	4	10:71–84	10:71–84	NOUN
ejpam-3759	266	5	,	,	PUNCT
ejpam-3759	266	6	2019	2019	NUM
ejpam-3759	266	7	.	.	PUNCT
ejpam-3759	267	1	[	[	X
ejpam-3759	267	2	2	2	NUM
ejpam-3759	267	3	]	]	PUNCT
ejpam-3759	267	4	m.	m.	NOUN
ejpam-3759	267	5	a.	a.	NOUN
ejpam-3759	267	6	ansari	ansari	PROPN
ejpam-3759	267	7	and	and	CCONJ
ejpam-3759	267	8	m.	m.	PROPN
ejpam-3759	267	9	r.	r.	PROPN
ejpam-3759	267	10	khan	khan	PROPN
ejpam-3759	267	11	.	.	PUNCT
ejpam-3759	268	1	notes	note	NOUN
ejpam-3759	268	2	on	on	ADP
ejpam-3759	268	3	(	(	PUNCT
ejpam-3759	268	4	m	m	PROPN
ejpam-3759	268	5	,	,	PUNCT
ejpam-3759	268	6	n	n	CCONJ
ejpam-3759	268	7	)	)	PUNCT
ejpam-3759	268	8	bi	bi	NOUN
ejpam-3759	268	9	-	-	ADJ
ejpam-3759	268	10	γ	γ	NOUN
ejpam-3759	268	11	-	-	PUNCT
ejpam-3759	268	12	ideals	ideal	NOUN
ejpam-3759	268	13	in	in	ADP
ejpam-3759	268	14	γ	γ	NOUN
ejpam-3759	268	15	-	-	PUNCT
ejpam-3759	268	16	semigroups	semigroup	NOUN
ejpam-3759	268	17	.	.	PUNCT
ejpam-3759	269	1	rend	rend	VERB
ejpam-3759	269	2	.	.	PUNCT
ejpam-3759	270	1	circ	circ	PROPN
ejpam-3759	270	2	.	.	PUNCT
ejpam-3759	271	1	mat	mat	NOUN
ejpam-3759	271	2	.	.	PUNCT
ejpam-3759	271	3	palermo	palermo	PROPN
ejpam-3759	271	4	,	,	PUNCT
ejpam-3759	271	5	60:31–42	60:31–42	PROPN
ejpam-3759	271	6	,	,	PUNCT
ejpam-3759	271	7	2011	2011	NUM
ejpam-3759	271	8	.	.	PUNCT
ejpam-3759	272	1	[	[	X
ejpam-3759	272	2	3	3	X
ejpam-3759	272	3	]	]	PUNCT
ejpam-3759	272	4	s.	s.	PROPN
ejpam-3759	272	5	bogdanovic	bogdanovic	PROPN
ejpam-3759	272	6	.	.	PUNCT
ejpam-3759	273	1	semigroups	semigroup	NOUN
ejpam-3759	273	2	in	in	ADP
ejpam-3759	273	3	which	which	PRON
ejpam-3759	273	4	some	some	DET
ejpam-3759	273	5	bi	bi	NOUN
ejpam-3759	273	6	-	-	NOUN
ejpam-3759	273	7	ideal	ideal	ADJ
ejpam-3759	273	8	is	be	AUX
ejpam-3759	273	9	a	a	DET
ejpam-3759	273	10	group	group	NOUN
ejpam-3759	273	11	.	.	PUNCT
ejpam-3759	274	1	review	review	NOUN
ejpam-3759	274	2	of	of	ADP
ejpam-3759	274	3	research	research	NOUN
ejpam-3759	274	4	faculty	faculty	NOUN
ejpam-3759	274	5	of	of	ADP
ejpam-3759	274	6	science	science	NOUN
ejpam-3759	274	7	-	-	PUNCT
ejpam-3759	274	8	university	university	NOUN
ejpam-3759	274	9	of	of	ADP
ejpam-3759	274	10	novi	novi	PROPN
ejpam-3759	274	11	sad	sad	PROPN
ejpam-3759	274	12	,	,	PUNCT
ejpam-3759	274	13	11:261–266	11:261–266	PROPN
ejpam-3759	274	14	,	,	PUNCT
ejpam-3759	274	15	1981	1981	NUM
ejpam-3759	274	16	.	.	PUNCT
ejpam-3759	275	1	[	[	X
ejpam-3759	275	2	4	4	NUM
ejpam-3759	275	3	]	]	PUNCT
ejpam-3759	275	4	k.	k.	PROPN
ejpam-3759	275	5	wattanatripop	wattanatripop	PROPN
ejpam-3759	275	6	;	;	PUNCT
ejpam-3759	275	7	r.	r.	PROPN
ejpam-3759	275	8	chinram	chinram	PROPN
ejpam-3759	275	9	and	and	CCONJ
ejpam-3759	275	10	t.	t.	PROPN
ejpam-3759	275	11	changphas	changphas	PROPN
ejpam-3759	275	12	.	.	PUNCT
ejpam-3759	276	1	fuzzy	fuzzy	ADJ
ejpam-3759	276	2	almost	almost	ADV
ejpam-3759	276	3	bi	bi	NOUN
ejpam-3759	276	4	-	-	NOUN
ejpam-3759	276	5	ideals	ideal	NOUN
ejpam-3759	276	6	in	in	ADP
ejpam-3759	276	7	semigroups	semigroup	NOUN
ejpam-3759	276	8	.	.	PUNCT
ejpam-3759	277	1	int	int	NOUN
ejpam-3759	277	2	.	.	PUNCT
ejpam-3759	278	1	j.	j.	PROPN
ejpam-3759	278	2	math	math	PROPN
ejpam-3759	278	3	.	.	PUNCT
ejpam-3759	279	1	computer	computer	NOUN
ejpam-3759	279	2	sci	sci	PROPN
ejpam-3759	279	3	.	.	PROPN
ejpam-3759	279	4	,	,	PUNCT
ejpam-3759	279	5	13:51–58	13:51–58	PROPN
ejpam-3759	279	6	,	,	PUNCT
ejpam-3759	279	7	2018	2018	NUM
ejpam-3759	279	8	.	.	PUNCT
ejpam-3759	280	1	[	[	X
ejpam-3759	280	2	5	5	NUM
ejpam-3759	280	3	]	]	PUNCT
ejpam-3759	280	4	k.	k.	PROPN
ejpam-3759	280	5	wattanatripop	wattanatripop	PROPN
ejpam-3759	280	6	;	;	PUNCT
ejpam-3759	280	7	r.	r.	PROPN
ejpam-3759	280	8	chinram	chinram	PROPN
ejpam-3759	280	9	and	and	CCONJ
ejpam-3759	280	10	t.	t.	PROPN
ejpam-3759	280	11	changphas	changphas	PROPN
ejpam-3759	280	12	.	.	PUNCT
ejpam-3759	281	1	quasi	quasi	VERB
ejpam-3759	281	2	-	-	DET
ejpam-3759	281	3	a	a	DET
ejpam-3759	281	4	-	-	PUNCT
ejpam-3759	281	5	ideals	ideal	NOUN
ejpam-3759	281	6	and	and	CCONJ
ejpam-3759	281	7	fuzzy	fuzzy	ADJ
ejpam-3759	281	8	a	a	DET
ejpam-3759	281	9	-	-	PUNCT
ejpam-3759	281	10	ideals	ideal	NOUN
ejpam-3759	281	11	in	in	ADP
ejpam-3759	281	12	semigroups	semigroup	NOUN
ejpam-3759	281	13	.	.	PUNCT
ejpam-3759	282	1	j.	j.	PROPN
ejpam-3759	282	2	discrete	discrete	PROPN
ejpam-3759	282	3	math	math	PROPN
ejpam-3759	282	4	.	.	PUNCT
ejpam-3759	283	1	sci	sci	PROPN
ejpam-3759	283	2	.	.	PROPN
ejpam-3759	283	3	cryptogr	cryptogr	PROPN
ejpam-3759	283	4	.	.	PUNCT
ejpam-3759	283	5	,	,	PUNCT
ejpam-3759	283	6	21:1131–1138	21:1131–1138	PROPN
ejpam-3759	283	7	,	,	PUNCT
ejpam-3759	283	8	2018	2018	NUM
ejpam-3759	283	9	.	.	PUNCT
ejpam-3759	284	1	[	[	X
ejpam-3759	284	2	6	6	NUM
ejpam-3759	284	3	]	]	PUNCT
ejpam-3759	284	4	r.	r.	PROPN
ejpam-3759	284	5	chinram	chinram	PROPN
ejpam-3759	284	6	.	.	PUNCT
ejpam-3759	285	1	on	on	ADP
ejpam-3759	285	2	quasi	quasi	ADJ
ejpam-3759	285	3	-	-	ADJ
ejpam-3759	285	4	gamma	gamma	ADJ
ejpam-3759	285	5	-	-	PUNCT
ejpam-3759	285	6	ideals	ideal	NOUN
ejpam-3759	285	7	in	in	ADP
ejpam-3759	285	8	gamma	gamma	NOUN
ejpam-3759	285	9	-	-	PUNCT
ejpam-3759	285	10	semigroups	semigroup	NOUN
ejpam-3759	285	11	.	.	PUNCT
ejpam-3759	286	1	scienceasia	scienceasia	PROPN
ejpam-3759	286	2	,	,	PUNCT
ejpam-3759	286	3	32:351–353	32:351–353	NUM
ejpam-3759	286	4	,	,	PUNCT
ejpam-3759	286	5	2006	2006	NUM
ejpam-3759	286	6	.	.	PUNCT
ejpam-3759	287	1	[	[	X
ejpam-3759	287	2	7	7	X
ejpam-3759	287	3	]	]	X
ejpam-3759	287	4	r.	r.	PROPN
ejpam-3759	287	5	chinram	chinram	PROPN
ejpam-3759	287	6	and	and	CCONJ
ejpam-3759	287	7	c.	c.	PROPN
ejpam-3759	287	8	jirokul	jirokul	PROPN
ejpam-3759	287	9	.	.	PUNCT
ejpam-3759	288	1	on	on	ADP
ejpam-3759	288	2	bi	bi	ADJ
ejpam-3759	288	3	-	-	ADJ
ejpam-3759	288	4	γ	γ	NOUN
ejpam-3759	288	5	-	-	NOUN
ejpam-3759	288	6	ideal	ideal	NOUN
ejpam-3759	288	7	in	in	ADP
ejpam-3759	288	8	γ	γ	NOUN
ejpam-3759	288	9	-	-	PUNCT
ejpam-3759	288	10	semigroups	semigroup	NOUN
ejpam-3759	288	11	.	.	PUNCT
ejpam-3759	289	1	songklanakarin	songklanakarin	PROPN
ejpam-3759	289	2	j.	j.	PROPN
ejpam-3759	289	3	sci	sci	PROPN
ejpam-3759	289	4	.	.	PROPN
ejpam-3759	289	5	techno	techno	PROPN
ejpam-3759	289	6	.	.	PUNCT
ejpam-3759	289	7	,	,	PUNCT
ejpam-3759	290	1	29:231–234	29:231–234	NUM
ejpam-3759	290	2	,	,	PUNCT
ejpam-3759	290	3	2007	2007	NUM
ejpam-3759	290	4	.	.	PUNCT
ejpam-3759	291	1	[	[	X
ejpam-3759	291	2	8	8	NUM
ejpam-3759	291	3	]	]	X
ejpam-3759	291	4	r.	r.	PROPN
ejpam-3759	291	5	a.	a.	PROPN
ejpam-3759	291	6	good	good	PROPN
ejpam-3759	291	7	and	and	CCONJ
ejpam-3759	291	8	d.	d.	PROPN
ejpam-3759	291	9	r.	r.	PROPN
ejpam-3759	291	10	hughes	hughes	PROPN
ejpam-3759	291	11	.	.	PUNCT
ejpam-3759	292	1	associated	associate	VERB
ejpam-3759	292	2	for	for	ADP
ejpam-3759	292	3	a	a	DET
ejpam-3759	292	4	semigroup	semigroup	NOUN
ejpam-3759	292	5	.	.	PUNCT
ejpam-3759	293	1	bull	bull	PROPN
ejpam-3759	293	2	.	.	PUNCT
ejpam-3759	294	1	amer	amer	PROPN
ejpam-3759	294	2	.	.	PUNCT
ejpam-3759	294	3	math	math	PROPN
ejpam-3759	294	4	.	.	PUNCT
ejpam-3759	295	1	soc	soc	PROPN
ejpam-3759	295	2	.	.	PUNCT
ejpam-3759	295	3	,	,	PUNCT
ejpam-3759	296	1	58:624–625	58:624–625	NUM
ejpam-3759	296	2	,	,	PUNCT
ejpam-3759	296	3	1952	1952	NUM
ejpam-3759	296	4	.	.	PUNCT
ejpam-3759	297	1	[	[	X
ejpam-3759	297	2	9	9	NUM
ejpam-3759	297	3	]	]	X
ejpam-3759	297	4	o.	o.	NOUN
ejpam-3759	297	5	grosek	grosek	NOUN
ejpam-3759	297	6	and	and	CCONJ
ejpam-3759	297	7	l.	l.	PROPN
ejpam-3759	297	8	satko	satko	PROPN
ejpam-3759	297	9	.	.	PUNCT
ejpam-3759	298	1	a	a	DET
ejpam-3759	298	2	new	new	ADJ
ejpam-3759	298	3	notion	notion	NOUN
ejpam-3759	298	4	in	in	ADP
ejpam-3759	298	5	the	the	DET
ejpam-3759	298	6	theory	theory	NOUN
ejpam-3759	298	7	of	of	ADP
ejpam-3759	298	8	semigroups	semigroup	NOUN
ejpam-3759	298	9	.	.	PUNCT
ejpam-3759	299	1	semigroup	semigroup	PROPN
ejpam-3759	299	2	forum	forum	PROPN
ejpam-3759	299	3	,	,	PUNCT
ejpam-3759	299	4	20:233–240	20:233–240	NUM
ejpam-3759	299	5	,	,	PUNCT
ejpam-3759	299	6	1980	1980	NUM
ejpam-3759	299	7	.	.	PUNCT
ejpam-3759	300	1	[	[	X
ejpam-3759	300	2	10	10	NUM
ejpam-3759	300	3	]	]	X
ejpam-3759	300	4	o.	o.	NOUN
ejpam-3759	300	5	grosek	grosek	NOUN
ejpam-3759	300	6	and	and	CCONJ
ejpam-3759	300	7	l.	l.	PROPN
ejpam-3759	300	8	satko	satko	PROPN
ejpam-3759	300	9	.	.	PUNCT
ejpam-3759	301	1	on	on	ADP
ejpam-3759	301	2	minimal	minimal	ADJ
ejpam-3759	301	3	a	a	DET
ejpam-3759	301	4	-	-	PUNCT
ejpam-3759	301	5	ideals	ideal	NOUN
ejpam-3759	301	6	of	of	ADP
ejpam-3759	301	7	semigroups	semigroup	NOUN
ejpam-3759	301	8	.	.	PUNCT
ejpam-3759	302	1	semigroup	semigroup	PROPN
ejpam-3759	302	2	forum	forum	PROPN
ejpam-3759	302	3	,	,	PUNCT
ejpam-3759	302	4	20:283–295	20:283–295	PROPN
ejpam-3759	302	5	,	,	PUNCT
ejpam-3759	302	6	1981	1981	NUM
ejpam-3759	302	7	.	.	PUNCT
ejpam-3759	303	1	[	[	X
ejpam-3759	303	2	11	11	NUM
ejpam-3759	303	3	]	]	X
ejpam-3759	303	4	o.	o.	NOUN
ejpam-3759	303	5	grosek	grosek	NOUN
ejpam-3759	303	6	and	and	CCONJ
ejpam-3759	303	7	l.	l.	PROPN
ejpam-3759	303	8	satko	satko	PROPN
ejpam-3759	303	9	.	.	PUNCT
ejpam-3759	304	1	smallest	small	ADJ
ejpam-3759	304	2	a	a	DET
ejpam-3759	304	3	-	-	PUNCT
ejpam-3759	304	4	ideals	ideal	NOUN
ejpam-3759	304	5	in	in	ADP
ejpam-3759	304	6	semigroups	semigroup	NOUN
ejpam-3759	304	7	.	.	PUNCT
ejpam-3759	305	1	semigroup	semigroup	PROPN
ejpam-3759	305	2	forum	forum	PROPN
ejpam-3759	305	3	,	,	PUNCT
ejpam-3759	305	4	20:297	20:297	NUM
ejpam-3759	305	5	–	–	PUNCT
ejpam-3759	305	6	309	309	NUM
ejpam-3759	305	7	,	,	PUNCT
ejpam-3759	305	8	1981	1981	NUM
ejpam-3759	305	9	.	.	PUNCT
ejpam-3759	306	1	[	[	X
ejpam-3759	306	2	12	12	NUM
ejpam-3759	306	3	]	]	X
ejpam-3759	306	4	h.	h.	PROPN
ejpam-3759	306	5	hedayati	hedayati	PROPN
ejpam-3759	306	6	.	.	PUNCT
ejpam-3759	307	1	isomorphisms	isomorphisms	PROPN
ejpam-3759	307	2	via	via	ADP
ejpam-3759	307	3	congruences	congruence	NOUN
ejpam-3759	307	4	on	on	ADP
ejpam-3759	307	5	γ	γ	NOUN
ejpam-3759	307	6	-	-	PUNCT
ejpam-3759	307	7	semigroups	semigroup	NOUN
ejpam-3759	307	8	and	and	CCONJ
ejpam-3759	307	9	γ	γ	NOUN
ejpam-3759	307	10	-	-	NOUN
ejpam-3759	307	11	ideals	ideal	NOUN
ejpam-3759	307	12	.	.	PUNCT
ejpam-3759	308	1	thai	thai	PROPN
ejpam-3759	308	2	j.	j.	PROPN
ejpam-3759	308	3	math	math	PROPN
ejpam-3759	308	4	.	.	PUNCT
ejpam-3759	308	5	,	,	PUNCT
ejpam-3759	308	6	11:563–575	11:563–575	NUM
ejpam-3759	308	7	,	,	PUNCT
ejpam-3759	308	8	2013	2013	NUM
ejpam-3759	308	9	.	.	PUNCT
ejpam-3759	309	1	[	[	X
ejpam-3759	309	2	13	13	NUM
ejpam-3759	309	3	]	]	PUNCT
ejpam-3759	309	4	k.	k.	PROPN
ejpam-3759	309	5	hila	hila	PROPN
ejpam-3759	309	6	.	.	PUNCT
ejpam-3759	310	1	on	on	ADP
ejpam-3759	310	2	regular	regular	ADJ
ejpam-3759	310	3	,	,	PUNCT
ejpam-3759	310	4	semiprime	semiprime	NOUN
ejpam-3759	310	5	and	and	CCONJ
ejpam-3759	310	6	quasi	quasi	ADJ
ejpam-3759	310	7	-	-	ADJ
ejpam-3759	310	8	reflexive	reflexive	ADJ
ejpam-3759	310	9	γ	γ	NOUN
ejpam-3759	310	10	-	-	PUNCT
ejpam-3759	310	11	semigroup	semigroup	ADJ
ejpam-3759	310	12	and	and	CCONJ
ejpam-3759	310	13	minimal	minimal	ADJ
ejpam-3759	310	14	quasiideals	quasiideal	NOUN
ejpam-3759	310	15	.	.	PUNCT
ejpam-3759	311	1	lobachevski	lobachevski	PROPN
ejpam-3759	311	2	j.	j.	PROPN
ejpam-3759	311	3	math	math	PROPN
ejpam-3759	311	4	.	.	PROPN
ejpam-3759	311	5	,	,	PUNCT
ejpam-3759	311	6	29:141–152	29:141–152	PROPN
ejpam-3759	311	7	,	,	PUNCT
ejpam-3759	311	8	2008	2008	NUM
ejpam-3759	311	9	.	.	PUNCT
ejpam-3759	312	1	[	[	X
ejpam-3759	312	2	14	14	NUM
ejpam-3759	312	3	]	]	PUNCT
ejpam-3759	312	4	a.	a.	NOUN
ejpam-3759	312	5	iampan	iampan	PROPN
ejpam-3759	312	6	.	.	PUNCT
ejpam-3759	313	1	note	note	NOUN
ejpam-3759	313	2	on	on	ADP
ejpam-3759	313	3	bi	bi	NOUN
ejpam-3759	313	4	-	-	NOUN
ejpam-3759	313	5	ideals	ideal	NOUN
ejpam-3759	313	6	in	in	ADP
ejpam-3759	313	7	γ	γ	NOUN
ejpam-3759	313	8	-	-	PUNCT
ejpam-3759	313	9	semigroups	semigroup	NOUN
ejpam-3759	313	10	.	.	PUNCT
ejpam-3759	314	1	int	int	NOUN
ejpam-3759	314	2	.	.	PUNCT
ejpam-3759	315	1	j.	j.	PROPN
ejpam-3759	315	2	algebra	algebra	PROPN
ejpam-3759	315	3	,	,	PUNCT
ejpam-3759	315	4	3:181–188	3:181–188	NUM
ejpam-3759	315	5	,	,	PUNCT
ejpam-3759	315	6	2009	2009	NUM
ejpam-3759	315	7	.	.	PUNCT
ejpam-3759	316	1	[	[	X
ejpam-3759	316	2	15	15	NUM
ejpam-3759	316	3	]	]	X
ejpam-3759	316	4	p.	p.	NOUN
ejpam-3759	316	5	m.	m.	NOUN
ejpam-3759	316	6	pu	pu	PROPN
ejpam-3759	316	7	and	and	CCONJ
ejpam-3759	316	8	y.	y.	PROPN
ejpam-3759	316	9	m.	m.	PROPN
ejpam-3759	316	10	liu	liu	PROPN
ejpam-3759	316	11	.	.	PROPN
ejpam-3759	317	1	fuzzy	fuzzy	ADJ
ejpam-3759	317	2	topology	topology	PROPN
ejpam-3759	317	3	i.	i.	PROPN
ejpam-3759	317	4	neighborhood	neighborhood	PROPN
ejpam-3759	317	5	structure	structure	NOUN
ejpam-3759	317	6	of	of	ADP
ejpam-3759	317	7	a	a	DET
ejpam-3759	317	8	fuzzy	fuzzy	ADJ
ejpam-3759	317	9	point	point	NOUN
ejpam-3759	317	10	and	and	CCONJ
ejpam-3759	317	11	moore	moore	PROPN
ejpam-3759	317	12	-	-	PUNCT
ejpam-3759	317	13	smith	smith	PROPN
ejpam-3759	317	14	convergence	convergence	NOUN
ejpam-3759	317	15	.	.	PUNCT
ejpam-3759	318	1	j.	j.	PROPN
ejpam-3759	318	2	math	math	PROPN
ejpam-3759	318	3	.	.	PUNCT
ejpam-3759	319	1	anal	anal	PROPN
ejpam-3759	319	2	.	.	PUNCT
ejpam-3759	320	1	appl	appl	PROPN
ejpam-3759	320	2	.	.	PROPN
ejpam-3759	320	3	,	,	PUNCT
ejpam-3759	321	1	76:571–599	76:571–599	NUM
ejpam-3759	321	2	,	,	PUNCT
ejpam-3759	321	3	1980	1980	NUM
ejpam-3759	321	4	.	.	PUNCT
ejpam-3759	322	1	[	[	X
ejpam-3759	322	2	16	16	NUM
ejpam-3759	322	3	]	]	X
ejpam-3759	322	4	m.	m.	NOUN
ejpam-3759	322	5	murali	murali	PROPN
ejpam-3759	322	6	krishna	krishna	PROPN
ejpam-3759	322	7	rao	rao	PROPN
ejpam-3759	322	8	.	.	PUNCT
ejpam-3759	323	1	bi	bi	ADJ
ejpam-3759	323	2	-	-	ADJ
ejpam-3759	323	3	quasi	quasi	ADJ
ejpam-3759	323	4	ideals	ideal	NOUN
ejpam-3759	323	5	and	and	CCONJ
ejpam-3759	323	6	fuzzy	fuzzy	ADJ
ejpam-3759	323	7	bi	bi	NOUN
ejpam-3759	323	8	-	-	NOUN
ejpam-3759	323	9	ideals	ideal	NOUN
ejpam-3759	323	10	of	of	ADP
ejpam-3759	323	11	γ	γ	NOUN
ejpam-3759	323	12	-	-	PUNCT
ejpam-3759	323	13	semigroups	semigroup	NOUN
ejpam-3759	323	14	.	.	PUNCT
ejpam-3759	324	1	bull	bull	NOUN
ejpam-3759	324	2	.	.	PUNCT
ejpam-3759	325	1	int	int	NOUN
ejpam-3759	325	2	.	.	PUNCT
ejpam-3759	326	1	math	math	NOUN
ejpam-3759	326	2	.	.	PUNCT
ejpam-3759	327	1	virtual	virtual	ADJ
ejpam-3759	327	2	inst	inst	PROPN
ejpam-3759	327	3	.	.	PROPN
ejpam-3759	327	4	,	,	PUNCT
ejpam-3759	327	5	7:231–242	7:231–242	PROPN
ejpam-3759	327	6	,	,	PUNCT
ejpam-3759	327	7	2017	2017	NUM
ejpam-3759	327	8	.	.	PUNCT
ejpam-3759	328	1	references	reference	NOUN
ejpam-3759	328	2	630	630	NUM
ejpam-3759	329	1	[	[	X
ejpam-3759	329	2	17	17	NUM
ejpam-3759	329	3	]	]	X
ejpam-3759	329	4	h.	h.	PROPN
ejpam-3759	329	5	rasouli	rasouli	PROPN
ejpam-3759	329	6	and	and	CCONJ
ejpam-3759	329	7	a.	a.	PROPN
ejpam-3759	329	8	r.	r.	PROPN
ejpam-3759	329	9	shabani	shabani	PROPN
ejpam-3759	329	10	.	.	PUNCT
ejpam-3759	330	1	on	on	ADP
ejpam-3759	330	2	gamma	gamma	PROPN
ejpam-3759	330	3	acts	act	NOUN
ejpam-3759	330	4	over	over	ADP
ejpam-3759	330	5	gamma	gamma	NOUN
ejpam-3759	330	6	semigroups	semigroup	NOUN
ejpam-3759	330	7	.	.	PUNCT
ejpam-3759	331	1	eur	eur	PROPN
ejpam-3759	331	2	.	.	PUNCT
ejpam-3759	332	1	j.	j.	PROPN
ejpam-3759	332	2	pure	pure	PROPN
ejpam-3759	332	3	appl	appl	PROPN
ejpam-3759	332	4	.	.	PUNCT
ejpam-3759	332	5	math	math	PROPN
ejpam-3759	332	6	.	.	PUNCT
ejpam-3759	332	7	,	,	PUNCT
ejpam-3759	332	8	10:739–748	10:739–748	NUM
ejpam-3759	332	9	,	,	PUNCT
ejpam-3759	332	10	2017	2017	NUM
ejpam-3759	332	11	.	.	PUNCT
ejpam-3759	333	1	[	[	X
ejpam-3759	333	2	18	18	NUM
ejpam-3759	333	3	]	]	PUNCT
ejpam-3759	333	4	m.	m.	NOUN
ejpam-3759	333	5	k.	k.	PROPN
ejpam-3759	333	6	sen	sen	PROPN
ejpam-3759	333	7	.	.	PROPN
ejpam-3759	334	1	on	on	ADP
ejpam-3759	334	2	γ	γ	NOUN
ejpam-3759	334	3	-	-	PUNCT
ejpam-3759	334	4	semigroups	semigroup	NOUN
ejpam-3759	334	5	.	.	PUNCT
ejpam-3759	335	1	lecture	lecture	NOUN
ejpam-3759	335	2	notes	note	NOUN
ejpam-3759	335	3	in	in	ADP
ejpam-3759	335	4	pure	pure	ADJ
ejpam-3759	335	5	and	and	CCONJ
ejpam-3759	335	6	appl	appl	NOUN
ejpam-3759	335	7	.	.	PROPN
ejpam-3759	335	8	math	math	NOUN
ejpam-3759	335	9	.	.	PUNCT
ejpam-3759	336	1	(	(	PUNCT
ejpam-3759	336	2	algebra	algebra	NOUN
ejpam-3759	336	3	and	and	CCONJ
ejpam-3759	336	4	its	its	PRON
ejpam-3759	336	5	applications	application	NOUN
ejpam-3759	336	6	,	,	PUNCT
ejpam-3759	336	7	new	new	ADJ
ejpam-3759	336	8	delhi	delhi	PROPN
ejpam-3759	336	9	)	)	PUNCT
ejpam-3759	336	10	,	,	PUNCT
ejpam-3759	336	11	91:301–308	91:301–308	NUM
ejpam-3759	336	12	,	,	PUNCT
ejpam-3759	336	13	1981	1981	NUM
ejpam-3759	336	14	.	.	PUNCT
ejpam-3759	337	1	[	[	X
ejpam-3759	337	2	19	19	NUM
ejpam-3759	337	3	]	]	PUNCT
ejpam-3759	337	4	m.	m.	NOUN
ejpam-3759	337	5	k.	k.	PROPN
ejpam-3759	337	6	sen	sen	PROPN
ejpam-3759	337	7	and	and	CCONJ
ejpam-3759	337	8	n.	n.	PROPN
ejpam-3759	337	9	k.	k.	PROPN
ejpam-3759	337	10	saha	saha	PROPN
ejpam-3759	337	11	.	.	PUNCT
ejpam-3759	338	1	on	on	ADP
ejpam-3759	338	2	γ	γ	PROPN
ejpam-3759	338	3	-	-	PUNCT
ejpam-3759	338	4	semigroup	semigroup	NOUN
ejpam-3759	338	5	-	-	PUNCT
ejpam-3759	338	6	i.	i.	NOUN
ejpam-3759	338	7	bull	bull	PROPN
ejpam-3759	338	8	.	.	PUNCT
ejpam-3759	339	1	calcutta	calcutta	PROPN
ejpam-3759	339	2	math	math	PROPN
ejpam-3759	339	3	.	.	PUNCT
ejpam-3759	340	1	soc	soc	PROPN
ejpam-3759	340	2	.	.	PUNCT
ejpam-3759	340	3	,	,	PUNCT
ejpam-3759	341	1	78:180–186	78:180–186	NUM
ejpam-3759	341	2	,	,	PUNCT
ejpam-3759	341	3	1986	1986	NUM
ejpam-3759	341	4	.	.	PUNCT
ejpam-3759	342	1	[	[	X
ejpam-3759	342	2	20	20	NUM
ejpam-3759	342	3	]	]	PUNCT
ejpam-3759	342	4	m.	m.	NOUN
ejpam-3759	342	5	siripitukdet	siripitukdet	NOUN
ejpam-3759	342	6	and	and	CCONJ
ejpam-3759	342	7	a.	a.	NOUN
ejpam-3759	342	8	iampan	iampan	PROPN
ejpam-3759	342	9	.	.	PUNCT
ejpam-3759	343	1	on	on	ADP
ejpam-3759	343	2	the	the	DET
ejpam-3759	343	3	ideal	ideal	ADJ
ejpam-3759	343	4	extensions	extension	NOUN
ejpam-3759	343	5	in	in	ADP
ejpam-3759	343	6	γ	γ	NOUN
ejpam-3759	343	7	-	-	PUNCT
ejpam-3759	343	8	semigroups	semigroup	NOUN
ejpam-3759	343	9	.	.	PUNCT
ejpam-3759	344	1	kyungpook	kyungpook	PROPN
ejpam-3759	344	2	math	math	PROPN
ejpam-3759	344	3	.	.	PUNCT
ejpam-3759	345	1	j.	j.	PROPN
ejpam-3759	345	2	,	,	PUNCT
ejpam-3759	345	3	48:585–591	48:585–591	PROPN
ejpam-3759	345	4	,	,	PUNCT
ejpam-3759	345	5	2008	2008	NUM
ejpam-3759	345	6	.	.	PUNCT
ejpam-3759	346	1	[	[	X
ejpam-3759	346	2	21	21	NUM
ejpam-3759	346	3	]	]	PUNCT
ejpam-3759	346	4	j.	j.	PROPN
ejpam-3759	346	5	p.	p.	PROPN
ejpam-3759	346	6	f.	f.	PROPN
ejpam-3759	346	7	solano	solano	PROPN
ejpam-3759	346	8	;	;	PUNCT
ejpam-3759	346	9	s.	s.	PROPN
ejpam-3759	346	10	suebsung	suebsung	PROPN
ejpam-3759	346	11	and	and	CCONJ
ejpam-3759	346	12	r.	r.	PROPN
ejpam-3759	346	13	chinram	chinram	PROPN
ejpam-3759	346	14	.	.	PUNCT
ejpam-3759	347	1	on	on	ADP
ejpam-3759	347	2	almost	almost	ADV
ejpam-3759	347	3	i	i	NOUN
ejpam-3759	347	4	-	-	PUNCT
ejpam-3759	347	5	ideals	ideal	NOUN
ejpam-3759	347	6	and	and	CCONJ
ejpam-3759	347	7	fuzzy	fuzzy	ADJ
ejpam-3759	347	8	almost	almost	ADV
ejpam-3759	347	9	i	i	NOUN
ejpam-3759	347	10	-	-	PUNCT
ejpam-3759	347	11	ideals	ideal	NOUN
ejpam-3759	347	12	in	in	ADP
ejpam-3759	347	13	n	n	CCONJ
ejpam-3759	347	14	-	-	PUNCT
ejpam-3759	347	15	ary	ary	NOUN
ejpam-3759	347	16	semigroups	semigroup	NOUN
ejpam-3759	347	17	.	.	PUNCT
ejpam-3759	348	1	jp	jp	PROPN
ejpam-3759	348	2	j.	j.	PROPN
ejpam-3759	348	3	algebra	algebra	PROPN
ejpam-3759	348	4	,	,	PUNCT
ejpam-3759	348	5	number	number	NOUN
ejpam-3759	348	6	theory	theory	NOUN
ejpam-3759	348	7	appl	appl	PROPN
ejpam-3759	348	8	.	.	PROPN
ejpam-3759	348	9	,	,	PUNCT
ejpam-3759	348	10	40:833–842	40:833–842	PROPN
ejpam-3759	348	11	,	,	PUNCT
ejpam-3759	348	12	2018	2018	NUM
ejpam-3759	348	13	.	.	PUNCT
ejpam-3759	349	1	[	[	X
ejpam-3759	349	2	22	22	NUM
ejpam-3759	349	3	]	]	PUNCT
ejpam-3759	349	4	k.	k.	PROPN
ejpam-3759	349	5	wattanatripop	wattanatripop	PROPN
ejpam-3759	349	6	and	and	CCONJ
ejpam-3759	349	7	t.	t.	PROPN
ejpam-3759	349	8	changphas	changphas	PROPN
ejpam-3759	349	9	.	.	PUNCT
ejpam-3759	350	1	on	on	ADP
ejpam-3759	350	2	left	left	ADJ
ejpam-3759	350	3	and	and	CCONJ
ejpam-3759	350	4	right	right	ADJ
ejpam-3759	350	5	a	a	DET
ejpam-3759	350	6	-	-	PUNCT
ejpam-3759	350	7	ideals	ideal	NOUN
ejpam-3759	350	8	of	of	ADP
ejpam-3759	350	9	a	a	DET
ejpam-3759	350	10	γ	γ	NOUN
ejpam-3759	350	11	-	-	PUNCT
ejpam-3759	350	12	semigroup	semigroup	NOUN
ejpam-3759	350	13	.	.	PUNCT
ejpam-3759	351	1	thai	thai	PROPN
ejpam-3759	351	2	j.	j.	PROPN
ejpam-3759	351	3	math	math	PROPN
ejpam-3759	351	4	.	.	PROPN
ejpam-3759	351	5	,	,	PUNCT
ejpam-3759	351	6	si:87–96	si:87–96	NUM
ejpam-3759	351	7	,	,	PUNCT
ejpam-3759	351	8	2018	2018	NUM
ejpam-3759	351	9	.	.	PUNCT
ejpam-3759	352	1	[	[	X
ejpam-3759	352	2	23	23	NUM
ejpam-3759	352	3	]	]	X
ejpam-3759	352	4	s.	s.	PROPN
ejpam-3759	352	5	suebsung	suebsung	PROPN
ejpam-3759	352	6	;	;	PUNCT
ejpam-3759	352	7	k.	k.	PROPN
ejpam-3759	352	8	wattanatripop	wattanatripop	PROPN
ejpam-3759	352	9	and	and	CCONJ
ejpam-3759	352	10	r.	r.	PROPN
ejpam-3759	352	11	chinram	chinram	PROPN
ejpam-3759	352	12	.	.	PUNCT
ejpam-3759	353	1	on	on	ADP
ejpam-3759	353	2	almost	almost	ADV
ejpam-3759	353	3	(	(	PUNCT
ejpam-3759	353	4	m	m	NOUN
ejpam-3759	353	5	,	,	PUNCT
ejpam-3759	353	6	n)-ideals	n)-ideal	NOUN
ejpam-3759	353	7	and	and	CCONJ
ejpam-3759	353	8	fuzzy	fuzzy	ADJ
ejpam-3759	353	9	almost	almost	ADV
ejpam-3759	353	10	(	(	PUNCT
ejpam-3759	353	11	m	m	PROPN
ejpam-3759	353	12	,	,	PUNCT
ejpam-3759	353	13	n)-ideals	n)-ideal	NOUN
ejpam-3759	353	14	in	in	ADP
ejpam-3759	353	15	semigroups	semigroup	NOUN
ejpam-3759	353	16	.	.	PUNCT
ejpam-3759	354	1	j.	j.	PROPN
ejpam-3759	354	2	taibah	taibah	PROPN
ejpam-3759	354	3	univ	univ	PROPN
ejpam-3759	354	4	.	.	PUNCT
ejpam-3759	355	1	sci	sci	PROPN
ejpam-3759	355	2	.	.	PROPN
ejpam-3759	355	3	,	,	PUNCT
ejpam-3759	355	4	13:897–902	13:897–902	NUM
ejpam-3759	355	5	,	,	PUNCT
ejpam-3759	355	6	2019	2019	NUM
ejpam-3759	355	7	.	.	PUNCT
ejpam-3759	356	1	[	[	X
ejpam-3759	356	2	24	24	NUM
ejpam-3759	356	3	]	]	PUNCT
ejpam-3759	356	4	l.	l.	PROPN
ejpam-3759	356	5	a.	a.	PROPN
ejpam-3759	356	6	zadeh	zadeh	PROPN
ejpam-3759	356	7	.	.	PUNCT
ejpam-3759	357	1	fuzzy	fuzzy	ADJ
ejpam-3759	357	2	sets	set	NOUN
ejpam-3759	357	3	.	.	PUNCT
ejpam-3759	358	1	inf	inf	PROPN
ejpam-3759	358	2	.	.	PUNCT
ejpam-3759	358	3	control	control	PROPN
ejpam-3759	358	4	,	,	PUNCT
ejpam-3759	358	5	8:338–353	8:338–353	NUM
ejpam-3759	358	6	,	,	PUNCT
ejpam-3759	358	7	1965	1965	NUM
ejpam-3759	358	8	.	.	PUNCT